This trophy is unlocked by completing any stage on the toughest difficulty. Keep in mind that cheats ARE disabled on this difficulty so unlike the other trophies, you can't just turn on God Mode and blast through the level (though if no clip mode is active when you start, it stays on). The rewind feature does stay enabled so use and abuse it if you're having difficulty beating a level on this difficulty. Pick a level you're most comfortable with, though I highly recommend the first level, "Hollywood Holocaust" as there is a trick that makes this easy.
From the start, hop down the hole and ignore the enemy on the crate. Head around the building to the back entrance (where you're normally supposed to enter) and you'll find a pig cop near here. Jump on his head and from there, hop onto the wall to your left (facing the doorway). From there, you can hop onto the ledge with the level exit. This trick will also net you the "Alien Maggots Are Gonna Pay" trophy.
For an excellent video demonstrating this technique, check out Smokeisdaman's run below. This video is not mine and is completely Smokeisdaman's.
https://www.youtube.com/watch?annotation_id=annotation_67618...