Go to the Bat Cave trophy room and head to the circular platform where you purchase red bricks. There are some objects under the stairs over a button you need to step on to light it green. Go up the stairs onto the platform and destroy the black container on it. Build the stand with the parts and pull the lever. Fly up to the top left side of the TV studio to find a silver block to destroy. Pull the lever revealed after. The brown crate will open with the character stud to collect.
Purchase the batman outfit in the character selector for 25,000 studs than select the character to change.