Complete the game and start on New Game+ to unlock all costumes.

Costume	How to unlock
Battle Armor of Ares	Complete the game and start on New Game+.
Battle Armor of Zeus	Complete the game and start on New Game+.
Fury Armor	Complete the game and start on New Game+.
Kraken Armor	Complete the game and start on New Game+.
Olive Skin Kratos	Complete the game and start on New Game+.
Skorpian Armor	Complete the game and start on New Game+.
War Armor of Hades	Complete the game and start on New Game+.