Here is the full list of all 18 Prince of Persia: The Two Thrones trophies - there are 1 bronze, 8 silver, 8 gold and 1 platinum.
Obtain all other trophies
Collect 10 000 Sand Credits
Complete the game on Hard
Complete the game in any difficulty without dying
Complete the game on Easy
Get all life upgrades
Complete the game on Normal
Kill the Vizier
Obtain all Sand Powers
Seal all the Sand Portals
Kill 100 enemies as the Dark Prince
Kill the two Bosses
Complete the horse cart sequences
Obtain all 6 Sand Tanks
Kill 100 enemies using a secondary weapon
Kill 50 enemies with a Speed Kill
Destroy 200 objects
Kill the Giant