She is insecure and tries to make herself feel better by being one-step better than everyone else.
The best thing to do is tell her you can't be her friend unless she discovers why she needs to one-up others and learns to base her self-esteem on her own accomplishments and how she can make the word a better place.
The likely result of this is that she'll get pissed off, not hang around you any more and tell other people you're a bitch. But there is a small chance she may take your advice, alter her style of thinking and become a good friend to you.
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