Shortly after emerging from the Phoenix Chamber and the encounter with the mysterious warrior, you'll be faced with the terrifying Kraken. After the cutscene, press the L3 and R3 buttons at the same time to activate the Rage of the Titans. Doing so will cause the Kraken to release Kratos. Press the L3 and R3 buttons again to preserve the Rage of the Titans meter. Start hacking away at the tentacle wrapped around the column on the left until the Kraken retracts it. At this point, carry the corpse that is in the middle of the area and place it on the button that was previously covered by the Kraken's tentacle.
When the switch is pressed down, the vent in the middle of the area will open, creating a steady source of steam. Use the steam from the vent to launch yourself towards the Kraken's head wound by gliding with the Wings of Icarus. While falling back down, use Cyclone of Chaos (L1 + Square) with Athena's Blades to deal damage. Continue doing this until the Kraken thrusts its tentacle into the vent.
At this point, approach the tentacle and move around to the front of it. Climb up to the top of the tentacle to reach a cap. Attack the cap until it breaks off. With the cap broken off, press the Circle button and Kratos will sever that tentacle. The Kraken will retract its damaged tentacle and push the corpse off of the button. Do the same thing to the Kraken in order to sever its right tentacle. Once you have attacked its head wound, the Kraken jams its right tentacle into the wall. Move to the end of the tentacle and jump up to grab hold of it. Sling across to the cap, attack it until it breaks off, and then press the Circle button to sever the tentacle.
Now is the time to empty the Rage of the Titans meter. Activate the Rage of the Titans and attack one of the Kraken's wrapped tentacles. When the Kraken retracts that tentacle, quickly move on to the other and attack that one. When the Kraken retracts its other tentacle, it will slump down from the platform, still hanging on feebly to the pillars. Pull the lever that is in front of the Kraken; the lever extends the bridge to the phoenix's platform, effectively mashing the dangling beast in the process.This video is from our unofficial game guide. You can view the full guide here