Here is the full list of all 13 Spartan trophies - there are 2 silver, 10 gold and 1 platinum.
You were born with a sword in your hand! You have killed 100 enemies using your sword.
You collected 5000 Coins!
You finished a level with all the coins collected!
You sure know how to use your shield! You have deflected 200 attacks.
First death. You got a Trophy for trying!
You are one truly awesome gamer!
You collected 15000 Coins!
You collected 50000 Coins!
You have conquered Sparta.
You have conquered Mount Olympus.
You have conquered Delphi.
You have conquered Hades.
You have finished all levels as King!