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