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