As you come down the elevator, pray she's far away. If she is, stay in the elevator and unload everything you've got right in her b**** face. When she starts walking towards you, pay attention; if she's between the two rocks on the left and right of the elevator, ****ing MOVE, her jump stomp will probably kill you (same routine for her energy beam, but you might be able to dodge the energy balls if possible). If you leave the elevator, alwys try to keep a rock between you and her, and try to keep an eye out because she may be distracted by the weak enemies that spawn in the back of the cave. If she's distracted, keep firing bullets. It takes a while, but be careful and quick and you'll kill her.
TL;DR If she's trying to kill you, run until she isn't. Shoot until she's trying to kill you, repeat process till boss is dead.
XBL GT: ShAd0wF1AmE (that's a zero in ShAd0w, not an O)
I gunzerked her with dual rockets on my normal playthrough <_< that was pretty much my solution to anything. Not dying? Better throw more explosions at it. I'm a firm believer that there's no problem in BL2 that can't be solved with more/bigger explosives.
Side note: I dropped myself to fight for your life a lot with tediore launchers on my first play through...