I had a friend like this. She didn't want to be my friend IRL, but acted like BFF on Facebook- which was super weird to me. Basically she is super annoying online.
So anyway, I tried deleting my account and starting over but I still let her be my friend in the new account, and tried to limit all of our mutual friends. But it still was too much, and I ended up defriending her. I know it sounds weird, but my life is much better now.
So the way I see it is- delete your account altogether, start a new account with no mutual acquaintances, limit what she can see, or defriend her. Good luck- FB is so annoying and drama filled. I would love to get rid of it altogether except my sis will share medical info on my nephews on FB and then not call to tell me about it, so I keep it just for that reason. Some people just don't understand how to use FB appropriately.