The Surge

Vanity pieces are all unlocked by using the modifiers during the episodes. There are 16 total mods and you must use all of them at least once. You can tell one has been used when the stars on the pictures change from black to gold, and the reward picture will have a check mark on it when you receive the reward. I had to use one mod three times before the vanity piece unlocked for some reason, but that may have been a fluke.

Most of the modifiers unlock just by completing the various episodes, though two have unique requirements. One is to basically chicken out before the boss fight, so after completing the two rooms you'll be on a catwalk with the entrance to the boss room ahead and an opening to the right that leads to the control room. Use the drop down to the right to keep your rewards, skip the boss, and unlock the mod. The other mod is unlocked by completing an episode with less than 10 kills. This is easily done in Episode 1 by using both shortcuts and running past any enemies not required to open a door.

On top of using each mod at least once, you also need to use a combination of two, three, and four mods specifically for unique vanity pieces. You'll get the Golden Dillon for using two mods, Going Feral for three, and Smirking Luchador for four. These don't stack, so this will take three seperate runs to unlock all three. Otherwise, once you've done those combinations and used all 16 mods at some point, you'll have the last vanity items.