Try doing it with Ammochain. It's a lot easier than you'd suspect. All you do is phase and then make your way to a corner, and then stand and chainfire, walking it back and forth over the enemies, wrecking them. I almost never use a shotgun for the City of Skulls, since I'm usually either doing a restricted game, melee, or Ammochain.
However, tac shotties will work very well indeed. RLs don't work too well, since the reload time will kill you and the RL's DPS is just way too low compared to a dedicated build. Not only that, but it's damage drops off too fast with range.