And so continues the blood bath. The DLC is certainly appropriately named, at least.
This mission is simple. Just grab a powerful shotgun, an armful of grenades, and obliterate everyone. You're gunning for badasses specifically, but don't show any quarter; blast everyone.
If you're having issues then get yourself upstairs, or into a corner. The patrons will scrap amongst themselves and letting them engage each other will give you ample opportunities to get the drop on any badasses amongst the rabble, obliterating them before they get a chance to think.
Another quick mission, then.