Killer Moth is faced in Act 4 of Episode 3 when you play as Batman and Robin.
To defeat Killer Moth, you need to build and power up the large generators in the foreground so that you can flip the switches which turn on the giant light bulb in the center of the room. Once the bulb comes on, he will take a hit of damage and drop back to the ground where you can reach him to deal additional punching damage.