Here is the full list of all 12 Delta Zero achievements.
Obtain a life upgrade.
Complete the game on any difficulty with Tempest Armor.
Complete the game on any difficulty with Pulse Armor.
Complete the game on Normal difficulty.
Complete the game on Hard difficulty.
Obtain a special weapon.
Obtain all life upgrades.
Obtain the secret armor upgrade.
Complete the game on Normal or Hard without dying.
Complete the game on Normal or Hard in less than 90 minutes.
Complete the game on Normal or Hard without obtaining any life upgrades.
Obtain all other achievements.