Perform these tasks in a level to unlock Zero's other forms:

Active Form: Kill 20 enemies with the Z-Saber while dashing
Defense Form: Kill 20 enemies with the Shield Boomerang
Energy Form: Grab 25 Life Capsules
Erase Form: Ricochet 30 shots from enemies with the Shield Boomerang
Power Form: Pull anything 30 times with the Chain Rod
Proto Form: Complete the game
Rise Form: Kill 20 enemies with the Jumping Slash in a stage
Ultimate Form: Use every Cyber Elf
X Form: Kill 50 enemies with Buster Gun