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