Here is the full list of all 36 God of War III trophies - there are 20 bronze, 10 silver, 5 gold and 1 platinum.
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Burn 100 enemies with the Bow of Apollo
Blind 100 enemies with the Head of Helios
Deliver 50 kicks to Hounds
Beat Titan Mode
Beat the Labyrinth without dying or failing
Perform a 1000-hit combo
Summon every Soul with the Claws of Hades
Beat the Challenge of Olympus
Completely upgrade all weapons
Collect all of the ‘Godly Possessions’
Successfully entertain Aphrodite
Beat the game
Kill Zeus
Solve the Three Judges
Collect all of the Phoenix Feathers
Collect all of the Minotaur Horns
Save Pandora
Collect all of the Gorgon Eyes
Acquire the Boreas Icestorm
Solve Hera's Gardens
Kill Cronos
Open the Gates of Tisiphone
Gut 3 Centaur Generals
Kill the Poseidon Princess
Kill Hercules
Kill Hermes and acquire his Boots
Kill Helios
Rip apart 1 Olympus Sentry
Sever Gaia’s hand
Cover Kratos in 500 buckets of blood by killing the enemies
Kill Hades
Discover the secret 'Hades Arm' room
Upgrade any weapon to the next level
Acquire the Bow of Apollo
Kill Poseidon