[Edit: I've gotten some good suggestions from the original poster in a short time. First, a round is 6 seconds and not 10. Well... that's an embarrassing brain fart. I'll adjust for that. (Though it does literally say, "about 6 seconds" so it could be 10 :D.) The OP also suggested that the character be maximized. That changes things as well but it doesn't change the overall results.]
Defending the Tarrasque? That's a laugh. In every edition up to 5e the tarrasque is THE monster to beat. There aren't any tougher or fiercer outside of Spelljammer weirdness. Most entries list it as a civilization killer. It's a walking 50 foot apocalypse with swords of sharpness for claws and a carapace that reflects your magic spells back at you.
Some, perhaps many, would say that the tarrasque has fallen on hard times in the fifth edition. Of course, it's not a pushover. The standard John Doe model tarrasque has 676 hit points, five attacks that do a minimum of 24 damage each, magic resistance, and three extra actions a round with its legendary actions. It is also immune to non-magical weapon attacks. Sadly, it's lost its regeneration from previous editions and its immunity to non-magical weapons can be overcome by any sort of magical weapon: it doesn't matter how many or few pluses the weapon has. Yes, the legendary tarrasque can now be damaged by a lowly +1 sword. How the mighty have fallen.
And how very low have they fallen indeed. Even unto contempt itself.
Case in point (and the reason I'm writing this post), I was privy sometime ago to a poster on facebook who claimed the tarrasque could be taken out by a first level player--perhaps even easily. Granted, most claims on the internet should be met with large doses of scepticism. Such a claim, on its face, seems to be one of those claims. However, since I am a neurotically fair-minded person I considered it, and had to admit there was more to it than what one might first imagine. That was a hard thing for me. Full disclosure--I'm a big fan of the tarrasque. I want it to live up to its 30 CR rating. Ok. Perhaps not so much a fan of the tarrasque, but I just want a DnD game where the challenge ratings are accurate. A 30 CR monster should mean a truly epic challenge that pushes the players to the ultimate limits of their ingenuity and courage. It should be a walking breathing Tomb of Horrors. If any first-level character, even one piloting a veritech, could take out a tarrasque, then the system is seriously broken.
For those who are anxiously biting their fingernails or those who have reached the point of TLDR, the reality is not as bad as the poster made out. However, it's not great. However again, it brings up some interesting realities about 5e DnD.
Anyhow, here's the scenario. Taking out the tarrasque at first-level requires a character that can fly and who is armed with a +1 bow. "Madness!" you cry. "No!" the poster would reply. +1 weapons are fairly easy to come by. What about flying? Pick an Aarakocra (id est--a birdman). How? Take your aarakocra, grab your +1 bow, fly out of range of the tarrasque (easily done since most tarrasques lacking a handy-dandy zeppelin strapped to their backs can't fly), and snipe the tarrasque till it dies. Of course, you can only hit it by rolling a 20, which means it would take a few hours--but the tarrasque can thus be more-or-less easily taken out by a first level character.
I forget what the rest of the conversation on the thread was like. I don't think too much was said. I think there was some math-hammering about how long the process would take. Some suggested having the tarrasque chuck some boulders at the birdman.
Let's touch on that last suggestion since it generated an interesting bit of controversy. Can the tarrasque make up for its lack of ranged attacks by chucking rocks etc. at its enemies? Of course it can. It really depends on how you envision it. If it has claws like a T-Rex then probably not. If it has claws like anything else then probably. I think such a tactic is perfectly acceptable. HOWEVER, I don't think it's acceptable if we are analysing the tarrasque. It has to be analysed as written. It doesn't have any throwing attacks like a giant might. Otherwise, we can come up with a bunch of weird scenarios to beef up our tarrasque. Perhaps we could give it a potion of fire-breathing? Perhaps we can give it a leaping attack? You see, all these extra scenarios distort the actual capabilities of the tarrasque. The rock throwing one seems reasonable but allowing it opens the door to more ludicrous--yet possible--scenarios like the zeppelin backpack scenario.
So we are back to square one for our beleaguered kaiju. If the tarrasque can't toss anything at the aarakocra sniper is it doomed?!
No. Let's get into some real analysis. First of all, let's consider the time it would take for our flying archer to take down the tarrasque (I think I'm about to set the world record for most-mentions of the tarrasque on a single page). One caveat however. I'm not sure my math is going to be perfect on this. It doesn't really need to be precise though, as it will generally show the problems with such a scenario.
Since our intrepid archer can only hit the tarrasque on a natural 20, it means that in the long run, and it's going to be a long one, our archer should be able to hit and damage the tarrasque once every twenty attack rolls, which also means once every twenty rounds. Assuming that our archer is armed with a +1 shortbow and not any other sort of ranged weapon, our archer should do 8 points of damage on every hit since a short bow does an average of 3.5 damage on each hit which would be doubled for a critical hit (so 7 points) and that's 8 with the +1 bonus. (We're not adjusting for possible stat bonuses because that brings up multiple scenarios which I don't care to calculate.) The tarrasque has 676 hit points so that will take 85 hits to drop the tarrasque and given that the archer bird will hit once every 20 rounds, it should take 85x20 or 1700 rounds. Each round is 6 seconds... 10 rounds in a minute.. 60 minutes in an hour... or 170 minutes or 2 hours and 50 minutes in total. (I think.)
Apart from the time commitment, this is also going to take 1700 arrows. 20 arrows weighs 1 pound. Arrows require a quiver and 20 arrows can fit into a quiver. 1700 arrows weigh 85 pounds and require 85 quivers, each of which weigh 1 pound. All-in-all the arrows and quivers alone weigh 170 pounds in addition to 2 pounds for the shortbow and that brings us to a minimum of 172 pounds that the aarakocra will need to fly around with. It's a point of trivia, but given the carrying rules the aarakocra will need at least a 12 strength to carry all that.
What does this all mean? This is where the rules start undermining this scenario. First of all, there is the problem of carrying all the arrows necessary to down the tarrasque. While the character might barely be able to carry all those arrows, they are going to need to be carried in 85 quivers. I think even the most fair-minded of DMs would have a problem with a single character sporting all that. The rules for aarakocra (aarakocrai?) specify that they can't fly while wearing medium or heavy armor. While it's not explicit, it's clear that either the weight or encumbrance of wearing those sorts of armor will keep an aarakocra grounded. Likewise, carrying 85 full quivers (if that is even possible) or even the weight of 85 full quivers should prevent the archer-bird from flying.
This brings us into another more-obvious problem for the scenario and which DMs can benefit from. Why has the player even been allowed to play an aarakocra (I hate spelling that) and why has it been given a +1 bow at first level? Granted, this is a theoretical scenario but the take-away for DMs is that you need to be very careful about what you allow into your games. Aarakocra, an optional race, have wisely been restricted from official play since having flight, especially at first level, is a very powerful ability. The same goes for magical items. Fifth edition has been designed to need a minimum of magical items at most levels. A number of classes even have means to make magical attacks in lieu of having a magical weapon, so the need is even less. Lesson: you don't need to allow any race or class that has been published. Certainly, a DM allowing an aarakocra to carry all these arrows is also stretching the rules past the point of breaking. You might as well allow the player to shoot death-rays from her eyes.
[[Edit: I originally made a mistake and calculated with rounds being 10 seconds each. This drops the scenario just below the 3 hour mark so this part is moot.] Second, looking at the rules for flying mounts in the DMG (pgs 119-120) we see that flying mounts need 1 hour of rest for every 3 hours of flight. It doesn't say how long characters can fly under their own power if they aren't constructs or flying by magic, but since an aarakocra is neither we are safe to assume they count as their own mounts and can only stay aloft for 3 hours maximum. Sadly for the aarakocra, landing means quickly becoming a tarrasque snack. Scenario over.]
This isn't the end, however. There is an even more important rule to take into consideration. The player needs to roll a natural 20 to damage the tarrasque. Given the time it will take to down the tarrasque and given the tragic laws of probability and statistics, this means the player will also be rolling as many 1s as they will be rolling 20s. Here's the sticking point about this. Considering the number of 20s you are going to need to roll to kill the tarrasque, each 20 is rather insignificant by itself. That is not the case for rolling a natural 1--a critical fumble. Given the absolute lethality of the tarrasque for a first-level character, it only takes one fumble to spell the character's end. When you also consider that the character should be rolling 85 natural 1s in the time it takes to kill the tarrasque, it should be plain that the archer will never get to that magical eighty-fifth natural 20. At the very least, the character will suffer a critical equipment failure which will mean they will be unable to complete the task of killing the tarrasque.
And there we have it--under close inspection it's impossible for our brave aarakocra archer to take down the tarrasque without some mind-boggling DM permissiveness.
So... all this was nerdy fun, but I hope you realise how ridiculous the whole exercise was. What was the point? The point is that while the hard design-realities of 5e's rules are going to make it impossible for a first-level character to take out a tarrasque... (ellipsis added for drama) many of the considerations that would stop a first-level character are easily overcome by higher-level characters. The tarrasque is a 30 CR creature. The CR rating means that the CR of a monster should present a worthy but not deadly challenge for a party of four characters of that equal level. For example, a 10 CR monster should be a moderate challenge for a party of four 10th level characters. The maximum level any character can attain in 5e is 20th level. The tarrasque, to repeat, is CR 30. As I've mentioned, that means the challenge of facing the tarrasque should strongly (if not overwhelmingly) tax the resources of even the most powerful party.
But does it in fantasy reality?
Consider the scenario of our poor aarakocra against the resources available to a 20th level character. At 20th level, characters should be ruling their own kingdoms (or equivalent thereof). At 20th level the characters should be able to call on all sorts of powerful allies and probably have a deity or three on speed-dial to call in some favours. At 20th level, it shouldn't be hard to have a character muster a small army of aarakocra archers all armed with magical bows. At 20th level, it shouldn't be hard for characters to have a small fleet of flying carpets or airships or airships armed with magical ballistas. At 20th level, the character's abilities should have expanded far beyond what they can do as individuals.
It's hard to imagine then, what challenge a tarrasque can really pose to a 20th level character. It will still be a hard fight. However, with a little preparation the players should be able to down a tarrasque unless the DM tosses in some other shenanigans.
This doesn't seem right for a CR30 monster. Consider an ancient Red dragon. It's 'only' CR24 but when compared to the tarrasque it presents much more of a threat to a party of 20th level characters. First of all, it has a ranged attack. Beyond that, it has a genius-level intelligence, superhuman-level charisma, a huge supply of resources it can draw from in its treasure horde, and lifespan of centuries or even millennia to develop and carry out its schemes.
In conclusion, what can we learn from all this?
Generally, we once again see that the CR system isn't an accurate gauge of determining challenge for a party--especially a high-level party.
Concerning the tarrasque itself, in other conversations I've seen about using the tarrasque, it isn't too much of a threat to a 20th level party unless the party is placed in unusual circumstances. (A tarrasque appears! You're all underground and naked!) What the tarrasque does make is a great wrecking-ball and centerpiece. By 20th-level the players should have evolved from murder-hobos and have invested in a few things in their fantasy world. It would seem that the tarrasque would be a great way to threaten that. The role of the characters, therefore, would be to intervene and stop the tarrasque from destroying the kingdom or whatever important mcguffin 20th-level characters care about. The tarrasque campaign, as we can see, probably requires some extra elements to hamper the characters efforts from stopping the tarrasque.
First of all, there shouldn't ever be a run of the mill tarrasque. It's CR30. The party should never encounter a mid-range tarrasque. It should always have maximum hit points and do maximum damage.
Even better, things should get really complicated when the tarrasque appears. Perhaps, the forces of evil decide to attack en masse when the tarrasque appears. They might have been responsible for unleashing the tarrasque or they might just be taking advantage of the opportunity. Perhaps there is a civil war going on in the players' realms. Perhaps the forces of nature, such as natural disasters, present the characters with an impossible choice--stop the tarrasque or help the victims. In short, if you are going to use the tarrasque in high-level campaigns it shouldn't be used as a direct threat to the characters, and it should be assisted by all sorts of complications that hamper the party from marshalling their full strength against it. The tarrasque should be an end-game challenge and retrospective of the characters' stories. For 20 levels the characters have been building up their stories. Ideally, the tarrasque should be a major part of a campaign that threatens everything the characters have done throughout their entire careers. Old allies should come forth; old enemies should reappear; long-term secrets should be revealed. In short, the tarrasque is less of an opponent and more of a narrative tool to sum up the totality of the players' lives.
[Push back: The OP suggested a maximized aarakocra fighter with a magical longbow (why not a magical hunting rifle or even an anti-matter rifle since the DM is being psychotically generous? They're in the DMG!) and archery fighting style. Ok. I can allow that. You can figure it out yourself. Long story short--it does radically drop the scenario time and amount of arrows the bird needs to carry, but numerous 1s will still be rolled to get there. Once again, it's not going to happen.]
[Counter-Pushback: Now that I think of it just because the tarrasque can't attack the maxed-out aarakocra sniper that doesn't mean it just has to stand there. From a pure mechanical perspective it can dodge or dash away. Dodging means the sniper bird attacks with disadvantage. That does two things. If I recall correctly disadvantage is equivalent to a -4 or -5 attack penalty. The aarakocra is most likely back to the same chances of only hitting it on a natural 20. That brings the required time and encumbrance back closer to my original calculations. Rolling with disadvantage also increases the chance of rolling a 1. Moreover, even though the tarrasque is using its action to dodge it can use a legendary action to finish the aarakocra off when it eventually rolls a 1 (which will probably be sooner than later). The tarrasque can also use dash and movement as a legendary action to outpace and outrange even a flying aarakocra with a longbow. With a 30 con it can either escape the fight altogether or if it kites the player (which it can probably do since the player in the scenario is committed to beating the tarrasque) it can stay in long range of the bow and the player will again be attacking with disadvantage. It can also kite the player and stay out of range (but still within sight) until the aarakocra is forced to land and rest for an hour--at which point it returns, overtakes, and eats our feathered hero.]
