If she's the same as the regular Ninja Gaiden, my best advice is to keep your distance. I was having trouble with her in the original on Normal mode... basically get my ass kicked each time (the save point isn't very far if you get the underwater one IIRC) many times. Then a buddy happen to stop by and said "uh try staying away from her" cause I was toe-to-toe with her most of my tries. So he says that and 2 minutes later I fvcked her up, first try with his new advice. However, I'm guessing I had a lot more potions than zero, so yeah I found in NG that you can beat most anything if you go back, farm essence, buy supplies. I don't think you'd need to load an old save, just go to a point where you are easily able to rack up essence (use the essence ring, and bats generally respawn every time and you can do UT to get a load of essence each time).
edit: The pink demon sucks hard and you only get like milliseconds of animation before you know she will do it. So you just can't stick in close to her... mostly attack her with flying swallow move then maybe one swing, then jump the fvck away. Sometimes she like takes a break on the ground for quite a few seconds so you can dish out some damage there. The pillars are a PITA but best avoived with a circular, roll-jump manuever. You can interrupt your roll (left trigger + analog direction) with a jump at any time I believe, so this comes in handy for avoiding boss attack. This probably works for the fireballs too. In fact, if you haven't gotten to the tank and helicopter yet, the roll-jump or something like roll-roll-jump-jump is the only way to survive on hard mode or worst!!
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