Cthulhu is capable of instant regeneration, from what I understand. He took a ship to the face and was back to 'perfect form' in a matter of moments. I'm not too sure Kratos has anything that can kill the Great Old One.
Uh, original Cthulhu is weak as hell. He got rammed by a steamship and was basically knocked out by it. He recovered, but it was by no means instant and it allowed the main character to get away. He also has no special powers, except normal humans eventually go insane after seeing him, but that can take months. He's just a huge bipedal squid thing with extremely low durability.
If you want to go by the piles and piles of Cthulhu fanfiction, (the stuff not written by Lovecraft) then he's a nearly omnipotent super being that would probably make Living Tribunal his working girl.
Going by the canon Cthulhu, Kratos tears him apart easily. If his regeneration is a problem, Kratos wins via soul ripping with the Claws of Hades.