First I make sure that I have enough fire rate with shotguns to hold off Barons in the Wall. That is, at least Finess*2 + Reloader (or some mod packs and shell box)
Then it depends on build, but I don't know how to beat Cathedral without at least Berserk, so, berserk. Juggler is always good, especially with melee.
My favorite builds are Vampyre, Sharpshooter and Shottyhead.
Gear - I usually make "tactical" everything. Boots, armor, shotgun.
Still don't have reliable strategy for Mortuary. I know running for nuclear BFG helps at prolonged sieges, as well as having nuclear plasma rifle, as well as clearing some patchess with skulls. And that worst case, I can do four Azrael blasts to kill all Viles, at a cost of 20 maximum health. But either way, above HNTR I end either dead (rarely) or nearly out of resources, so I have to do reast of the game with nuclear weapon, melee and handful of remaining ammo/medpacks.