I've seen a good bit of conflicting information on this creature. Is it possible to actually kill it? Permanently?
Is the answer to this something that varies from edition to edition of D&D?
Actually, the Tarasque is an imaginary creature in a game, so you can't actually kill it since it's not real.
Joking aside, in DnD 3.0 you had to reduce it to -30 and use a Wish spell to kill it permanently, otherwise it inevitably regenerated. The entry in the Monster's Manual states that anything else which normally would kill instead just reduces it to -10hp.
In the 4th edition Monster's Manual, it's listed under Abomination, and now lives in the world's core, returning there to sleep when it reaches 0hp; there are no rules to kill it, though it is suggested that - if the Tarrasque leaves the world - it could be killed.
In 5e the Tarrasque is pretty tame by comparison: no regeneration or choice to not take full damage from an attack. That said, you need to do 676 damage against its AC25; it's immune to poison, fire, and nonmagical weapons; it reflects back ranged spells and some others. So you've got to get crawling on it with magical weapons and touch spells. Don't worry, though--if you get swallowed but your fellows manage to kill it, you can crawl out with 30' movement. So not only is it possible to kill the 5e Tarrasque, but it's been explicitly contemplated in the rules.
So it does seem to vary from edition to edition.
I’ll toss a 3.5-specific answer in there: yes, and it’s pretty trivial if you can justify a fair bit of knowledge of its defenses and vulnerabilities, as well as those of a select few creatures and items in the world. The Tarrasque in 3.5 is basically a puzzle monster: it’s immune to a ton of stuff, devastating in melee, and can only be completely killed by wish, but if you know these things it’s pretty easy to kill.
Most importantly, you need to know about the Tarrasque itself, its powers and weaknesses, which is not something you’re going to get through a Knowledge check directly, in all likelihood, since at 48 HD the Tarrasque’s going to need a DC 58 Knowledge (arcana) check. So on some level this does depend on DM fiat, but ultimately facing the Tarrasque always does.
Anyway, assuming you know what the Tarrasque is (and more importantly, is not) immune to, and that you’ll need wish to finish it, here’s what to do.
First, you need a party at level 3, at least one of whom is a Wizard. They need to have appropriate wealth for their level, and that wealth needs to be reasonably liquid and they need to be able to pool it to buy a specific item.
The first thing to find are some Allips. These are CR 3 incorporeal undead with a Wisdom-draining touch attack. They have 4 HD. You need to know they exist, you need to know they have that Wisdom-drain ability, and you need to know where to find them. All of this should be within the realm of possibility for a level 3 Int-based character who maxes his Knowledge (religion) ranks and has the use of a decent library or whatever; the base DC to identify an Allip is 14, and 24 will get you at least two bits of information about them. Clearly someone who knows the details of the Tarrasque’s strengths and weaknesses should be able to figure this out.
You then need to use command undead on some, and you will need to win your opposed Charisma checks which might be rough since the Allip has 18 Cha. You won’t be asking it to do anything that puts it in danger, but you will want it to follow you around and drain something for you. Various tricks used to make planar binding easier may be useful for accomplishing the check, but simply having a reasonable Charisma will work if you can find a good supply of Allips. Even if you fail, the spell will protect you from them à la charm so as long as you can figure out where to find some Allips, this should be OK. You will only need six of them to obey you anyway, and there’s only going to be one command for each of them.
Note that at level 7, you can cast summon undead IV for Allips, and at level 8 (or equivalent if you can find boosters) Rebuke Undead can control them, which is a bit better than command undead.
Anyway, you then need to get a Candle of Invocation. At 8,400 gp, this is well beyond a single character’s wealth, but a party of four 3rd-level characters could pool their wealth to buy one. Crafting one is out of the question at this level, and for good reason.
If you need a single individual’s wealth to afford a Candle of Invocation, that’s 5th level, and if a single item cannot be more than a quarter of one’s wealth that’s 9th level. Of course, various wealth-breaking tricks can be used to get Candles of Invocation at any level you like.
Lastly, you need to find the Tarrasque itself and get the Allips to it. This is actually the trickiest part of the whole thing, considering how fast the Tarrasque is capable of moving, but assuming the thing is not literally charging from place to place, it should be do-able. Worst comes to worst, set up a distraction that can hold it in place for a few rounds. Having some method of flight, though difficult at this level, is really strongly recommended since the Tarrasque cannot fly. Being incorporeal, burrowing, or earth-gliding all work just as well.
Once the Allips descend on the Tarrasque, there is no contest. Its Touch AC is 5, its Wisdom is 14, it is not immune to ability drain, and it has no way of attacking the Allips since they are incorporeal and the Tarrasque’s natural weapons, for all they count as Epic for the purposes of overcoming Damage Reduction, are not magical and therefore do not have even the 50% chance of hitting the Allips. In four to fourteen attacks (on average, six), the Tarrasque is unconscious and going to stay that way unless some damn fool decides to cast restoration on it.
An unconscious Tarrasque is a threat to no one, but someone evil and/or suicidal might decide to cast restoration on it. Before that happens, hire a bunch of warriors with scythes to coup de grace it. Each coup de grace does an average of 20-28 damage depending on how much Strength you can get out of them, so that’s 5-13 damage after its DR. Twenty-eight of these guys can line up around a Colossal creature like the Tarrasque, so that’s an average of 140-364 damage per round. You can speed things up by also throwing in some guys with glaives (average 15.5-21.5, or 0.5-6.5 after DR) to stand around the guys with scythes. We can fit thirty-six of those for 8-234 average damage per round. Anyway, subtract 40 per round from these for Regeneration, and the rest is nonlethal.
The men cost 1 sp each per day (they need no training for this), or 3 sp per day if you want some training. Figure you hire trained guys for the day; it’s a pittance anyway. Have one of the party members be a Paladin for Aura of Courage and another be a Bard for Inspire Courage and Diplomacy to get them over of any fears they might have about this (the Bard can also dramatically improve the damage rates above). Scythes are 18 gp each, glaives are just 8 gp each. In total, 28 scythers and 36 glaivers is a mere 811 gp and 2 sp. On average, if everybody’s got 10 Strength and we don’t include Inspire Courage, that’s 108 damage per round, so give them a minute or so of hacking away at the beast before you move on (they should continue coup de grace’ing until you finish killing it just so it doesn’t regenerate).
Now comes the Candle of Invocation. One of its functions is to cast gate as the spell, at 17th Caster Level. Gate, the spell, is capable of Calling and controlling a single creature of a given type with HD up to twice gate’s Caster Level. You’re looking for an immediate task, so “you need not make any agreement or pay any reward for the creature’s help,” it just happens.
Anyway, gate in one of the many creatures that gets wish as a spell-like ability: a solar probably won’t mind helping rid the world of this force of destruction, djinn and efreet are traditional and you can even get another two wishes (hint: offer it the opportunity to get its own wish made on the third wish if it performs the first two wishes without twisting them), and so on. Not that gate gives the called creature much opportunity to have an opinion on the commands given to them, but since these are powerful creatures that you really don’t want to give a reason to call on you rather than the other way around, it pays to pick your ally here wisely. Plus twisting a wish is all about abusing the letter of the wish given, which means it’s pretty easy to be as obedient as gate forces you to be while still ruining some idiot’s day.
Congratulations, the Tarrasque is dead. All it cost you was 9,211.2 gp, money you could have easily made up with that second genie wish if you wanted. That’s assuming you aren’t getting huge rewards for, ya know, killing the Tarrasque.
For completeness: Pathfinder has the Regeneration-ability for the Tarrasque defined as follows.
Regeneration (Ex) No form of attack can suppress the tarrasque's regeneration—it regenerates even if disintegrated or slain by a death effect. If the tarrasque fails a save against an effect that would kill it instantly, it rises from death 3 rounds later with 1 hit point if no further damage is inflicted upon its remains. It can be banished or otherwise transported as a means to save a region, but the method to truly kill it has yet to be discovered.
So in Pathfinder it is also not possible to kill it forever.
Killing the tarrasque permanently in AD&D 2nd edition is much the same as in 3rd edition—get it to –30 hp and then use a wish spell—except the part of the creature's description that talks about this couches it in terms that put the instructions in doubt.
Phrases like, "Legend says that…", and, "Slaying of the tarrasque is said to be possible only if…" leave it open to being changed by the DM, and the players can never be certain that the tarrasque will stay dead, even if they do just as the legends say.
The Monster Manual II for AD&D 1st edition also has the same or similar vague phrasing:
The slaying of the tarrasque is said to be possible only if the monster is reduced to -30 or fewer hit points and a wish for its death then used.
Then more 'Legend says...' phrasing about the treasure that could be obtained if it was slayed.
The easiest way in 3.5e or Pathfinder is to teleport him to the positive energy plane. The tarrasque will regen until explode in a pure energy disruption. From the d20srd.org on the Positive Energy Plane:
Despite the beneficial effects of the plane, it is one of the most hostile of the Inner Planes. An unprotected character on this plane swells with power as positive energy is force-fed into her. Then, her mortal frame unable to contain that power, she immolates as if she were a small planet caught at the edge of a supernova. Visits to the Positive Energy Plane are brief, and even then travelers must be heavily protected.
Pathfinder shares the same text.