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