Please note that you must have all of these characters at the same time. If you retire one past level 5 and then get the others to 5, it will not work until you re-create the retired one again. You must have them all as current non-retired characters at level 5+ for the achievement to pop. The classes needed are just the 4 classes you get immediately from Jaws of the Lion:
Hatchet
Red Guard
Demolitionist
Voidwarden