Dash: She does a back flip then dashes straight at you. Simply dash off to one side to avoid her.
Grab: She can stab you with her tail and then fling you off to the side. This only happens if you get really close to her, so be aware of that.
Combos: She has a five hit combo where she throws a quick series of punches and claw swipes. You can easily block the initial attack and then Reverse Wind to dash away. She also has several other combos where she stabs you with her claws or swipes at you with her tail. In all cases, they have pretty similar reach and power, so stay alert and be ready to block and dash.
Teleporting Dash Attack: She can teleport away from your attacks and then teleport back to you and immediately attack right after she appears. Keep your guard up and be ready to dash behind her.
Blood Attack: She will summon a massive heart in the air above her that will shoot streams of blood at you. Not only do they do substantial damage to you, but they can also heal her. Either run away and keep moving or use a ninpo spell for its invulnerability frame. Occasionally, Art of the Inferno will actually hit her at this point.
Strategy: Since Elizébet has both ranged and close attacks, there really isn't a safe place in this fight. You can really only hurt her if you're close to her though - she'll almost always dodge ninpo and projectiles. To that end, stay close to her and constantly stay on the move to avoid her attacks. Once she finishes a combo, she'll be vulnerable for a brief moment, so hit with a quick combo of your own. I prefer to use the attack of the Eclipse Scythe because it's fast and does reasonable damage. Don't get greedy and try to extend the combo because she will likely hit you with her grab attack.