The Kraken is one heck of a beasty, as our previous hands-on will attest. But during a hands-on with a brand new demo at Gamescom, the developers explained to me exactly how to kill him. And I'd like to share that with you. See? Totally got your back.
So let's see what you're up against. It's a big sort of octopus beast, with all the traits you'd expect. Tentacles, flying.... Wait. Flying? Yes. Seeing as the levels aren’t full of water, it wouldn't make for a very good Kraken chase if he was just flapping about on the ground, would it? This means he can flee very effectively by swimming through the air. Accordingly, most of his moves are ranged attacks designed to push assailants away, because once you get up-close and personal, he's not so special. There lies his weakness.
So the Trapper on your team is your key weapon and needs to keep the Kraken from fleeing gunfire. The most effective tactic is to activate a large energy dome over the immediate area. Anything inside stays inside until it comes down.
Secondly, the Kraken can be tethered, during which he can't fly away and is forced to the ground. Of course, those swishing tentacles that can break the tether (which is flagged up on the Kraken player's screen, lit up brightly and with instructive text). But, while it's busy thrashing about, it isn't attacking or eating creatures to level up. So keep it occupied and contained as best you can.
The other thing to do is to stick together. A determined Kraken can take out a lone enemy relatively easily. But stick in a group spread out just wide enough to avoid his vortex attack. Then two or even three players have a good chance of keeping the hits raining in.
Keep doing that and, eventually, he's bound to (ahem) 'krak'.
Check out the following slides for additional images and more information.