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