The Maiden and Hunger have achieved some measure of parity in this conflict. She dodges better and has much better healing, he only needs a few hits to finish her. Of course neither are going to simply wait things out, there are still cards they have to play. Were this a simple fight between normal humans instead of whatever these two are, I would tend towards having Hunger unleash as much power as possible immediately and try to kill her quickly, before she has a chance to reveal her trap.
But this fight is as much narrative as it is physical and magical. And trying to gain an advantage so soon just sets Hunger up for the inevitable upset when she unleashes her hidden weapon.
Also, Hunger hasn't revealed his true scheme yet, the Age & Treachery we know and love him for. To have the most impact, it needs to happen at his lowest point! When all seems lost and the Maiden is utterly sure of her victory, he would be all "you fell for it" and show her that you don't fuck with Tyrants.
So stall and show weakness, feed her ego and her arrogant belief in her victory, right until it's time for a decisive strike.
[X] The Cavalry
I feel a bit bad about risking our Companions for this, and even worse for this choice echoing that first fight against the original Tyrant, where his friends sacrificed themselves one after another for a slim chance at victory, but they're all in this together, sharing both weal and woe.