Put the shadow warrior's body n top of the yellow button again to re-open the vent and go to it. Use the Icarus Wings to glide up to the head and do a good bit of damage with aerial attacks. Keep repeating this until the next mini-cutscene.
The Kraken will use a hardened spear attack that goes across its body and the arena, eventually getting stuck in a wall.When this happens head to the south west section of the room and double jump to hang from the bottom of the tentacle. head north east to find another ring. Cut that off to expose the flesh beneath. You should then be able to get that second tentacle.