You will need to acquire each costume and use its special ability once in battle to unlock the achievement. The costumes, their general locations and the abilities are listed below.
** Any character in the party can equip a costume and execute the moves, it doesn't have to be the party leader and it doesn't need to be done more than once. Thanks to merbear and z for asking.
** Noteworthy is you CAN backtrack to retrieve any pieces you may have missed, prior to beating the final boss.
Robot (start the game with) – Ability: Missile Barrage
Knight (obtained when Everett joins) – Ability: Guardian Shield
Statue of Liberty (obtained by finding three costume pieces in Auburn Pine, design given by kid at the house party) – Ability: Anthem
Space Warrior (obtained by finding three costume pieces in Auburn Haven Mall, design given by security guard) – Ability: Meteor Avalanche
Ninja (obtained by finding three costume pieces in Auburn Haven Mall, design given by group of kids in ninja costumes guarding third level of mall) – Ability: Kitsune Shroud
Unicorn (obtained by finding three costume pieces in Auburn Haven Mall) – Ability: My Pretty Panacea
French Fries (obtained by speaking to the french fry vendor in Auburn Haven Fall Valley) – Ability: Salt Assault
Pumpkin (obtained by speaking to the green glowing scarecrows “Dorrion?” throughout the story starting in the cemetery on the way to Auburn Haven Mall from Auburn Pine) – Ability: All Hallows’ Eve
Vampire (obtained by finding three pieces in Auburn Haven Fall Valley, design given by speaking to the carnival ticket booth vendor) – Ability: There’s a Bat in My Hair
Black Cat (obtained by finding all the Creepy Treat Cards in the game) – Ability: The Cat’s Meow
BiLLzThEd0n has indicated a thread link that can help you obtaining the pieces for the
Vampire and Unicorn costumesCredit to
Epsilon Theta for updting the link
Please comment if there's anything you feel should be added to help other gamers out and I'll include an edit with credit to you.