Imagine for a moment that her behaviour and attitude is a reaction of something. Perhaps one of your parents act that way and she's picked that up? Or perhaps her friends do. Or perhaps your own behaviour is somehow causing this. Maybe when you were both younger something happened. Try to step into her shoes and look at hte world from her point of view. Seek first to understand then to be understood. Perhaps she is striving to be equal with you in the family because she doesn't feel she is? What can you and perhaps your parents do to make her feel that way? Perhaps you could tell her that she is as equal as you (or other siblings, if you have them). Looking back on it, my parents always made the point of saying that we are all equal and they love us equally, however we are each unique and have our own strengths and weaknesses.
You might consider having a serious conversation with her about your relationship and her behaviour. It'd help to have some good communication books to help you (like Difficult Conversations or Messages).
Another thing that I wholeheartedly recommend is listening and just being there without judging, as well as doing something nice for her.
Yet another thing that you might consider is get her a copy of one of your favourite PD books. Or 7 Habits of Highly Effective Teens (the teen version is written by the son). I just got a copy for my sister and she loves it. I'm planning to get another one for my brother.
Hope something here helps.
