Here is the full list of all 31 Shadow of the Colossus trophies - there are 18 bronze, 6 silver, 6 gold and 1 platinum.
Acquired all Trophies
Acquire all items available in hard time attack
Clear the game in hard difficulty
Max out stamina bar
Acquired all fruits in the world
Reached top of the shrine
Killed all shining lizards
Acquire all items available in normal time attack
Perform all stunt riding using Agro
Clear the game in normal difficulty
Endure being sucked into the light for over 1 minute in the ending
Defeat 16th Colossus
Save at all save points
Hang onto the hawk for more than 30 seconds
Hang onto the fish for over 30 seconds
Defeat 15th Colossus
Defeat 14th Colossus
Defeat 13th Colossus
Max out HP bar
Defeat 12th Colossus
Defeat 11th Colossus
Defeat 10th Colossus
Defeat 9th Colossus
Defeat 8th Colossus
Defeat 7th Colossus
Defeat 6th Colossus
Defeat 5th Colossus
Defeat 4th Colossus
Defeat 3rd Colossus
Defeat 2nd Colossus
Defeat 1st Colossus