First beat BSB to open the door. Sneak behind her and go for visceral. Once she aggros, back off go into Oeden by the dweller/ or down the stairs behind chapel dweller. She should go back to her spot and de-aggro. Rinse and repeat viscerals. At about half health she will just chase you and not de-aggro. Make sure she is close following but not too close and take the elevator up to the wheelchair dude. She should fall into the hole and die. Quit out and her badge should be on the ground.

You can pull this off when she isn't half health but it means she might de-aggro or get on the elevator with you. Half health guarantees she'll follow from a distance with you sprinting.