Here is the full list of all 36 God of War: Chains of Olympus trophies - there are 20 bronze, 10 silver, 5 gold and 1 platinum.
Push flaming cart to the top
Kill the Basilisk
Upgrade any weapon
Entertain the Persian harem
Kill the Persian King
Finish all beam walks
Cause the Basilisk to retreat
Defend the Shores of Attica
Collect all of the trophies
Kill Charon, the Ferryman
Push away Calliope
Sacrifice powers
Kill Persephone
Chain the Titan, Atlas
Finish parry puzzle
Acquire the Triton Lance
Find ballista secret
Break the Chains of Tartarus
Move the Titan, Hyperion
Running across the long chain
Acquire Gauntlet of Zeus
Awaken all three horses
Collect all the Gorgon Eyes
Collect all the Phoenix Feathers
Completely upgrade all weapons and magic
Execute a 200-hit combo
Slit 50 Satyr throats
Parry 50 attacks
Break out of stone status 5 times in a row
Don't push away Calliope for one minute
Watch the movie "Atlas and Persephone" three times
Beat the Challenge of the Gods
Execute a 1000-hit combo
Play the game with an unlocked costume
Beat the game
Beat the game (Hard Mode)