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