You need to participate in a Contest before you get Cosplay Pikachu. It doesn't matter if you win or lose the contest. After it's over, Lisia will talk to you, then when you exit the dressing room and head toward the exit of the building, a woman will come up to you and give you Cosplay Pikachu (note that if you have a full party, Cosplay Pikachu will be sent to your Box, and you'll need to go to the Name Rater to nickname it).
You can return to the dressing room to change costumes/abilities of pikachu.