Complete the Game
After you finish the game for the first time, you unlock a wealth of different features. You can now play as the Spud of War, giving Kratos a potato-shaped costume that increases his magic ability--and also looks kind of silly. The costumes are available when you start a new game, when you are asked if you want to keep your upgrades. You can now play through the game in God Mode, which does not make Kratos invincible, but instead is the most challenging difficulty setting available. You also can watch a handful of movies, one about the making of the game at Ready At Dawn studios, as well as all of the in-game cut-scene movies. You're also able to look at the concept art for all of the characters. The first of the Challenges of Hades, a series of five increasingly difficult battles, will be opened to you.
Complete the Challenge of Hades
Play through the first Challenge of Hades and you'll unlock the next one. Each level unlocks the next, and if you manage to pass all five of Hades' challenges, you will be again rewarded with some new things, such as another costume, McKratos. This costume, in addition to the humorous look, increases your attack skill, making you a more formidable foe. You will also have access to the environmental concept art, and a movie about the Lost Levels. For assistance with the Challenges of Hades, some hints and tricks to help you pass them, consult the guide under References
Complete God Mode
If you beat the game in God Mode, you will be rewarded with another handful of fun features. The Mime of War costume, which puts Kratos in the typical white face paint of the mime and boosts his Red Orb gathering, is the final unlockable costume. In addition, you can watch a video, the "Making of Attica," and look at some entertaining outtakes concept art.