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