She filled him full of arrows in all the right places so as to not kill him, because she obviously didn't want to/couldn't kill him. And while we'll never know for sure, I don't think she would have shot him there either.
Oh well… Like I said- I didn't like her as a character, so I don't have to miss her. It was just sad in that moment watching one of my favorite characters have to go through that. In fact, now that I think about it, Jon Snow might be my favorite character. The only other contenders would be Arya or Tyrion.