Just let Chibi run out of energy, and you'll wake up in your house wearing the trauma suit.
Run out of battery 5 times. The easiest way to do this is by using the Trauma suit's pose by hitting Z.
Drake Redcrest Suit:
Talk to Drake in the living room at night.
Squirt the frog in the backyard with water. The squirter is under the TV in Jenny's room.
Complete the Free Ranger missions.
Super Chibi-Robo Suit:
Thanks to Revolution Readers Levi and RoboRobo!