I spent bleeding ages trying to get all the doubles. Couldn't do it. I then finally realised that I didn't need to. The bitch is up on the cliff right above where you come through the painting. All you need do is climb up, sneak behind her and throttle the bitch.
I will have to try it again. I wonder how hard it is to do without any of the outsider skills, as you have a choice at the beginning to not accept them.