They go down to shotguns like a hot knife through butter. I'm pretty sure they're weak to sharpnel damage. Not to mention that you can get most of them in your cone of fire. (By the way, they're resistant to bullet and fire damage.)
By the way, the City of Skulls is a pretty extreme challenge. You don't have to do it (and probably shouldn't) without at least shottyman and/or a tactical shotgun. Without a shotgun build I'd feel much safer with a super shotgun. Or, you know, a melee build. Or like, a nuclear plasma rifle..