Simply complete the normal game on any difficulty to unlock the first Challenge of Hades. There are subsequent challenges that are, in turn, unlocked by completing the challenge before it.
Unlockable: Image Galleries
Characters
Complete the game on any difficulty.
Environments
Complete all Challenges of Hades.
Outtakes
Complete the game on God Mode difficulty.
Unlockable: Videos
In-Game Movies
Complete the game on any difficulty.
Inside Ready at Dawn Studios
Complete the game on any difficulty.
Credits
Turn the game on.
The Lost Levels
Complete all Challenges of Hades.
Making of Attica
Complete the game on God Mode difficulty.
Unlockable: Bonus Costumes
Spud of War
Complete the game on any difficulty.
McKratos
Complete all Challenges of Hades.
Mime of War
Complete the game on God Mode difficulty.
Unlockable: God Mode
Before you wet yourself in excitement, God Mode in God of War does not make you invincible. On the contrary, God Mode is the most difficult setting of the game. Fortunately, unlocking it isn't that difficult—just complete the game on any of the three standard difficulty settings.