Here is the full list of all 13 Spartan achievements worth 1,000 gamerscore. It takes around 15-20 hours to unlock all of the achievements on Xbox One.
You need to finish all levels as King.
Collect 5000 Coins.
Collect 15000 Coins.
Collect 50000 Coins.
Finish a level with all the coins collected.
Deflect 200 attacks.
Kill 100 enemies using your sword.
Finish all Sparta Levels.
Finish all Mount Olympus Levels.
Finish all Delphi Levels.
Finish all Hades Levels.
Finish the game.