Challenge Of The Titans Mode
Complete the game on any difficulty mode to unlock in the treasures section.
Exactly like the Challenge Of The Gods mode from the first God Of War, except there are 7 challenges.

Unlock Titan difficulty mode
Simply complete the game on any other difficulty mode.

Arena Of The Fates
Receive Titan rank on The Challenge Of The Titans to unlock in the Treasures section.
Kind of a practice mode where you choose the health/magic/abilities/enemies, ect.

Bonus Play
To Start a new game with all Weapons/Magic at the levels you completed the game at, simply save your game and start a new game. Choose the Bonus Play option and you can start a new game with all your weapons/Magic at the levels you beat the game with. You can only choose the Bonus Play option on the difficulty you've beaten the game on. They will be marked by a sword on the New Game screen.

Sex Mini-Game
A little while into the area of Rhodes, the first area of the game, you will drop down into a bath-house/sauna type area. Instead of continuing and diving down, jump out of the water onto the area around it. There should be two screens which are breakable. Behind one of the screens are two topless women. By walking up to them and pressing the circle button, you initiate the sex mini-game in which you complete a series of button presses. When you have won, you will receive a large amount of red orbs and some green orbs. You can only receive the orbs once, however you may play the mini-game as much as you'd like.