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 Labyrinth without dying or failing
Beat the game
Kill Zeus
Solve the Three Judges
Deliver 50 kicks to Hounds
Save Pandora
Completely upgrade all weapons
Acquire the Boreas Icestorm
Collect all of the Minotaur Horns
Solve Hera's Gardens
Collect all of the Gorgon Eyes
Summon every Soul with the Claws of Hades
Collect all of the ‘Godly Possessions’
Collect all of the Phoenix Feathers
Kill Cronos
Open the Gates of Tisiphone
Gut 3 Centaur Generals
Successfully entertain Aphrodite
Kill Hercules
Burn 100 enemies with the Bow of Apollo
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
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
Unlock all trophies
Perform a 1000-hit combo
Blind 100 enemies with the Head of Helios
Beat the Challenge of Olympus
Beat Titan Mode