You can run by all of that up the stairs if you want. You do not have to fight it. But, A little wind ninpo to get essence going then UT constantly will yield massive karma points as well as money. This area to me is actually the funnest part of the entire game.
For Elizebet, You can stay a good distance from her and use a full UT from the Scythe and it will take her down for a safe fight or you can use wind-run + flying swallow to knock her on her knees (only works when she is in flight) and then quickly switch to the LS and use a B + B + very brief pause to start B + B again quickly and she will never get back up.
Never argue with an Idiot. He'll only bring you down to his level and beat you with experience.