VIDEOS:
Muggshot
Muggshot's boss fights in the series all revolve around finding something capable of actually hurting the big lug since his massive muscles make melee weapons or punches simply bounce off Muggshot with no effect. You either have to use methods that outright bypass his defense (the aforementioned sunlight or shock pistol rounds) or hit him with something tougher than he is.
Example of:
Puzzle Boss