Complex sentence: He soon becomes the (unknowing) slave of Munk (a skinny, quiet mobster), who has Colosso (who is nicknamed "Big Boy" by the mobsters) break into the safe for them.
Split into simpler sentences: He soon becomes the (unknowing) slave of Lunk: a skinny, quiet mobster. Lunk has Colosso (who is nicknamed "Big Boy" by the mobsters) break into the safe for them.