So after some experimentation, I think I understand how the combat works.
Aside from base damage being determined by attack and defense, there are "true" strikes and parries/blocks depending on if you use the shield or parrying dagger. Basically, if you click with your mouse just before your attack lands or just before Alice's attack lands, you will hit harder or take less damage / no damage. This works for your basic attack, your head breaker ability, and all of Alice's attacks that aren't quick time events (so it doesn't work for headscissor/facesitting).
So to beat her. You want to lose a few times to get to level 5 (that's the max level, and you'll need the stats). Make sure you buy armor from Herba for every equipment slot and equip it using the equipment tab. Buy plenty of health potions (10 would be safe).
I don't think you can beat Alice without being able to guard and true strike at least a few times so practice that. For weapons I used the spear and parrying dagger instead of a shield. The spear counter attacks her whenever you parry, and the parrying dagger makes it so parried attacks deal no damage which adds up.
For alice's quick time event attacks (headscissor / facesitting), you have to press the key that shows up on screen using your keyboard before the little ring reaches the circle. It's not about timing, just hit it before you run out of time. If you run out of time, you're stuck and there is no getting out. The headscissor will kill you every time. The facesitting wont kill you, but you take a lot of damage and it will ruin your S rank for that attempt.
My fight strategy was to only use basic attacks and drink health potions whenever I was missing at least 100hp. You want to stay as healthy as you can and not waste SP until it's time to burn her. Once she drinks her health potion (around 30%), use your headbreaker ability as much as you can and try to kill her before she beats you. Someone already mentioned it, but if you drink any potion after she drinks hers, she will steal yours. She only does this once, so if you really want to try and drag the fight out, you can trick her by drinking an SP potion, but I found it was easier to just rush her.
Edit: after further experimentation, it seems you can also use your keyboard instead of clicking with the mouse to parry. I only tested the space bar, but other keys might work as well.