Watch Him Die

The watchers required to be kept alive for this achievement can be stunned, but they CANNOT be CC'd by shackles, traps or fears.
The watchers are also standing quite close to the entrance, making kiting difficult and/or pointless.

All three of the watchers have two common abilities:
Infected Bite - Disease cast on target, deals damage both on hit and on ticks. Should obviously be cleansed immediately.
Web Wrap - Random target stun, the stun can be removed by attacking the web.

The three watchers special specific abilities are:
Watcher Silthik - Poison Spray - Poisons the entire party, poison cleansing totem is defenitely recommended.
Watcher Narjil - Blinding Webs - Disorients the entire party for 5 seconds. Stuns can (and should) be used to interrupt the cast.
Watcher Gashra - Enrage - Enrages himself, attacking much quicker but slightly weaker. Should be countered by a stun or tranquilizing shot.

Krik'Thir himself frenzies, curses (decursable!) and mind flays, all making this a very challenging achievement.

What my group did was very simple... We managed to do it in 2 tries. What we did was we cleared to first boss without killing the critters (for a reason).
Our group comp was
Feral druid
Prot warrior (me)
Resto druid
Assassination Rogue
Ret pally

What i did, as the warrior, was (using a system of macros) shoot the watcher in the middle, Heroic throw the one on the right, and body pull the one on the left. I used bloodrage (for small amounts of initial aggro).I then intervened the feral druid (stealthed), Charged a spider, and intercepted a roach. This got me halfway up the hallway with the adds. I then turned around, Shield wall + shield block, when that ended, last stand + enraged regen and popped both trinkets, stoneform (since i'm a dwarf), and potted. I lasted about 40 seconds with all the adds on me. Shockwave is your friend, since they all are stunnable. While i did this, the feral druid tanked the boss while everyone else dpsed their brains out. Once i died, the adds started running back towards the group, and since the boss was dead, both druids shadowmelded and the rogue vanished, leaving the poor ret pally to die XD.

Basically, kite to entrance and live for as long as possible :). I've done it for 4 separate groups using this strategy.
Good luck ^.^

OK, here is by far the easiest way to do this achievement.

What you need: a boomkin (gear doesn't matter), a reasonably geared tank, and 3 DPS in the 3k+ range (preferably including a shaman but this is not required)

How it's done: Everyone groups up at the entrance to Krik'thir's cave, a little bit to the right of the tunnel. The boomkin needs to get as close as possible to the mobs without aggroing them. Have him cast Starfall, which pulls every mob in the room -- possibly including the boss if he's close enough, so the tank needs to be ready with taunt. The boomkin needs to wait for about 2 pulses of Starfall to make sure all 3 mini-boss packs are aggroed. Then he needs to turn his feathery butt around and Dash up the tunnel as fast as he can! If he's quick, he should be out of LOS before he can be web wrapped. Meanwhile, the tank and 3 DPS rush the boss, with the tank popping CDs to stay alive. If the boomkin needs the achievement, he can let the mobs kill him at the entrance, otherwise he can simply zone out; either way, the tank and DPS have plenty of time to kill Krik'thir before the trash comes back. We killed him with easily 10 seconds to spare, using a shaman.

This method works MUCH better than zerging. I spent a lot of time, frustration and repair bills trying to zerg this achievement with an Ulduar-geared tank, healer, and DPS. While we did get very close a couple of times, the wrong person always ends up getting web wrapped and killing your chances. By contrast, the above method is extremely easy and works 100% of the time if done right. We two-shotted it, after an initial mishap figuring out the pull. It also has much lower gear requirements and doesn't require any specific comp other than a boomkin (who doesn't even have to be geared -- any random scrub can do that part, or any random druid who doesn't mind respeccing for one fight, even if they've never played boomkin before).