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.
Upgrade any weapon to the next level
Acquire the Bow of Apollo
Kill Poseidon
Rip apart 1 Olympus Sentry
Unlock all trophies
Discover the secret 'Hades Arm' room
Kill Helios
Kill Hermes and acquire his Boots
Successfully entertain Aphrodite
Sever Gaia’s hand
Open the Gates of Tisiphone
Save Pandora
Solve the Three Judges
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
Cover Kratos in 500 buckets of blood by killing the enemies
Gut 3 Centaur Generals
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