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
Summon every Soul with the Claws of Hades
Save Pandora
Acquire the Boreas Icestorm
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
Deliver 50 kicks to Hounds
Kill Hercules
Burn 100 enemies with the Bow of Apollo
Kill Hermes and acquire his Boots
Kill Helios
Sever Gaia’s hand
Cover Kratos in 500 buckets of blood by killing the enemies
Rip apart 1 Olympus Sentry
Kill Hades
Upgrade any weapon to the next level
Acquire the Bow of Apollo
Kill Poseidon
Unlock all trophies
Discover the secret 'Hades Arm' room
Perform a 1000-hit combo
Collect all of the Gorgon Eyes
Collect all of the Phoenix Feathers
Collect all of the Minotaur Horns
Completely upgrade all weapons
Beat the Challenge of Olympus
Beat Titan Mode
Collect all of the ‘Godly Possessions’
Beat the Labyrinth without dying or failing