To hit the woman you have to make sure your Tetsugan wepon thingy is on the Kunai like object and not the blunt one, you have to aim for her waist, her neck and her feet. I think its four time around her waist, twice around the neck and twice around the feet, but i guess it depends how good you are at tightening the wire. Gain the three keys that she will drop then head for Akemi. A huge snake will appear out of no where and throw you back, the snake woman will challenge you again. This time stay on one platform and let her come to you, only attack when she is on your plat form and how in the air, Beware attacks from above. When you have yet again defeated the woman, aim your tetsugan for the rock above the huge snakes head, and tug on it untill it falls.