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