Raging RavenShe'll eventually overheat and go chill out on one of the roofs. She'll actually say "Gah, I'm overheating!" and all attacks will cease. You will find her more easily by using the night vision and looking around from the top level of the tower. If you haven't killed many of her flying-around buddies, they'll be circling around her location.

While she's cooling down, that's your opportunity to send a rocket her way or snipe her. If you don't have a rocket or a sniper or its relative ammo, you can always buy one. You should have enough DP to purchase one right there.

Since the B&B Bosses are in 2 parts, I don't think it counts as a 'kill' if you defeat their beast form with a lethal weapon. Though I could be wrong, but it wouldn't make sense to me.

You can still damage her normally as she's flying around, though it's easier to get bigger damage using that method. I found that if I just laid down on some stairs near the top level, she couldn't hit me at all, so you can use that if you need to regain your gauges.

It might be different on difficulties higher than 'Solid Normal'.