I had nothing to do with the below video. It does them in a weird order, but it's the best at telling you where to find the unicorn and Vampire pieces.
Robot: Awarded in the story.
Knight: Awarded in the story.
Statue of Liberty: Story-related.
Space Warrior: Story-related.
Ninja: Awarded in the story.
Pumpkin: Talk to the Green glowing scarecrows. They're mostly obvious.
Unicorn: See Video
Vampire: See Video
French Fries: Awarded in the story.
Black Cat: See
Completing this achievement earns the Black Cat outfit.
Each of the powers must be used in a fight. Any character may use the costume. Grubbin does not have a power and you can't use him in a fight (If you try, he's replaced with another costume). The unicorn and Statue's healing abilities may be used even if no one is injured. The achievement will unlock while the final attack animation is playing.