So to unlock this achievement will acquire a few things.
-Complete the game
-Unlock all towers
-Unlock all heads
-Gold Star all levels
In order to do this, talk to all the NPC’s as you progress through the game. This will help you unlock the heads.
Update: Bonus levels not required for 100%. Thanks Icy!
Now to gold star a level, you must complete the level without losing a life. You will know you accomplished this because it will have a golden shimmer sort of look to it.
If you can manage all that, this achievement will pop. Good luck guys.
Edit; decided I will give tips on how to gold star levels as I unlock them myself.
Update 2: Blade just mentioned bonus missions can be used to replace boss missions for the 100% completion achievement. Not sure if that was intended but might want to act fast before you have to go the boss route if your struggling with them