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