I've managed to beat it within 6 loops round 15. 
Stance
Stance
Skill (I feel like I wasted the loop learning this one since I never really used it in my winning fight)
Reflex (Dodge+hit) 
Reflex (Ha missed me, I sure won't) 
Reflex (Can't touch this fine piece and I know how you dance)

So yeah, that's all it takes. They got hit with the catapult and I managed to hit every time with a few crits.