Get good at avoiding.
At first, she'll be firing a straight laser, and occasionally an orb that creates a platform. You want to be ready to jump as soon as you see her move her hand, to jump over the laser if it shows up.
Later, when she's flying around, she has two common attacks: two lasers at you, and a spread-beam with the safe spot below her. To avoid the two lasers, jump away from her and they'll miss you.
Once you're good at avoiding and not dying immediately, you'll want to use your magic (C attack) to break her shield. Doing this makes her retaliate with beams from the ceiling, so I've found it best to do so during her first phase, when she's still predictable. If you can break her shield, though, she'll stop retaliating. I preferred the down+C attack. Once she's flying around and with the shield gone, you can just spam down+C and A to recharge to take her out quickly.
Same sort of strategy works on the final boss.
