Here is the full list of all 35 God of War III Remastered trophies - there are 18 bronze, 11 silver, 5 gold and 1 platinum.
Beat the game
Kill Zeus
Solve the Three Judges
Collect all of the Phoenix Feathers
Completely upgrade all weapons
Save Pandora
Acquire the Boreas Icestorm
Solve Hera's Gardens
Kill Cronos
Rip apart 1 Olympus Sentry
Open the Gates of Tisiphone
Gut 3 Centaur Generals
Successfully entertain Aphrodite
Kill Hercules
Kill Hermes and acquire his Boots
Kill Helios
Cover Kratos in 500 buckets of blood by killing the enemies
Sever Gaia’s hand
Kill Hades
Upgrade any weapon to the next level
Discover the secret 'Hades Arm' room
Acquire the Bow of Apollo
Kill Poseidon
Unlock all trophies
Perform a 1000-hit combo
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
Collect all of the Gorgon Eyes
Collect all of the Minotaur Horns
Beat the Challenge of Olympus
Beat Titan Mode
Collect all of the ‘Godly Possessions’
Beat the Labyrinth without dying or failing