Here is the full list of all 15 Zack Zero trophies - there are 13 bronze, 1 silver and 1 gold.
Finding all Nahirg treasures.
Finish the game in any difficulty level.
Finishing the rock and lava cave level.
Reach Zack's suit level 20.
Finishing the cave level.
Kill 50 enemies using each of Zack’s powers.
Use the power of your rock punch to kill 50 enemies.
Use rock spikes to kill 50 enemies.
Completing the Nahirg's base level.
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.
Kill 100 enemies using the flame thrower.
Killing 100 enemies with the blade launcher.
Find 5 nahirg treasures.