Here is the full list of all 15 Zack Zero achievements.
Finish the game.
Finding all Nahirg treasures.
Finishing the rock and lava cave level.
Finishing the cave levels.
Reach Zack's suit level 20.
Use the power of your rock punch to kill 50 enemies.
Kill 50 enemies using each of Zack’s powers.
Completing the Nahirg's base levels.
Use rock spikes to kill 50 enemies.
Killing 100 enemies with the blade launcher.
Killing a Nahirg general using only the blade launcher.
Kill 100 enemies using the flame thrower.
Finishing the outside of the Nahirg’s planet level.
Use frozen air to freeze 50 enemies.
Find 5 nahirg treasures.