You don't strictly need Hell Break, but... okay, that's a lie. You definitely need Hell Break if you want to beat Daji in less than half an hour. In order to get Hell Break, you need to master the fire magic and the attack buff (PSI Megido and Limit Break). Hell Break pretty much is the cheese- it's so strong, once you have it you can cheese the entire game.
You'll need 111 SP total to get it. If you don't have the SP for it, take the time to max out your affection with all the demons you've befriended. Each one gives 10 SP at max friendship. I would also recommend levelling up Cool Calm as much as you can. Making Ecstasy no longer a factor is a huge advantage. Make sure you have Hell Break and Cool Calm up every turn- the moment one wears off, refresh them both.
Have you been using Sylph Storm throughout the game? If you have, good. Don't use it. In fact, unlevel it and refund the SP to put into other spells. All Sylph Storm does is help you dodge physical attacks, and physical attacks only hurt your Willpower. With Hell Break, you don't ever need to worry about your Willpower getting low. At this point in the game, Sylph Storm has outlived its usefulness.
For the Beast phase, keep a careful watch on what she's doing each turn. If she does the time symbol thingy, use defensive posture. If she lowers her body and builds up power in her legs, use evasive posture. And if you get caught, use violent rage instead of regular struggle every time. Your Willpower is constantly being restored by Hell Break, it doesn't matter how much Willpower it costs.
Don't get impatient. It might seem alluring to skip out on refreshing one of your spells in favour of getting one more attack in, but that's a slippery slope to losing. Just keep chipping away. It's a war of attrition, and you've got the advantage.