As soon as the fight starts, grab the "eye key" in the middle of the room and begin running around the outside until you can match it to the proper door. You can unlock it, but will not be able to go through until you damage her enough. I use The Dentist throughout this entire battle since she will always be in the air and moving, just lock on to her and fire away. She will occasionally spawn enemies, but nothing too tough to deal with.
Once you do enough damage, she will go through the door you unlocked and start the final phase of the battle. It's an endless hallway with a section of light that is attached very close to her, so it is key to always be moving forward or else you'll be in darkness. She does not change her attacks, and will spawn enemies here too, though I try to ignore them to not fall behind. Same strategy as before works great, use the lock on with The Dentist and shoot her, once all four wings are destroyed, you defeat her.