Once in the chamber with the Kraken, first defeat the normal enemies and then taunt him by swimming in front of one of the four columns (they will have target arrows in the middle where you can't get at them. The Kraken will pound the ground in front of the pillar where you are located (try to dodge as he strikes) and it will take a chunk out of the front of the stand beneath the pillar. Swim into the middle of that broken stand, where the arrow is.
You immediately switch to a mini-game where your active character must then dodge the Kraken in a random sequence. Just before each opportunity to dodge, a button will show on the screen. Press that button and the next button will show. After 4 or 5 of these, the Kraken will knock down the pillar, causing it to fall on his head which will take his health bar down by 25% per pillar.
You need to repeat this cycle for each pillar.. Kill the regular enemies, taunt the Kraken, do the mini-game.
If he pounds the pillar and it does not seem to be taking damage, check the other pillars that remain standing. There is a good chance one of them already has the front knocked out and this happens for only one column at a time. Also, while dodging and weaving, if the Kraken shoots ink missiles at you, you can block them with no damage by holding LB until they are gone.