LEGO BATMAN 3 BEYOND GOTHAM

You can use either lab, in the Watchtower or Batcave for this.

I used the one in the Batcave... as you enter from the Watchtower, come toward the screen as far as you can, then head to screen right across the black and yellow bridge. Go up the steps and straight ahead into the Character Customizer room.

Once in there, step into either of the two customizing machines at the top of the stairs.

In the machine, select a slot (I just used Custom A), randomize it's appearance and abilities, name it something besides "Custom A" (this may not be necessary, but I did it anyway), and make sure you hit the Y button for "Use Current Character", or the achievement won't pop. I had changed my character a half dozen times without doing this, and wasn't getting the achievement until I did that.