My friend thinks she's better than me! PLEASE HELP!?

My friend is so frustrating to deal with! She constantly brags about what a wonderful singer she is and how our glee club would fall apart without her. She cant handle it when she finds out im better at her at something. When she found out i was stronger, she started working out, then when i told her that my dad teaches me karate, she got super mad and said i was bragging and that my dad just probably taught me sloppy technique, then she shoved me into a wall shouting, "WHERES YOUR INSTINCT NOW!!!" and she did it in front of everyone. She likes to create competitions, like sometimes we'll have drawing competitions, and even when ive clearly won, she'll say, "well i think mines better." When i say something that i think is funny, she'll shout. "THAT JOKE ISNT GOING ANYWHERE!" She constantly punches me and pinches me and shoves me into walls, but if i hurt her once, shell turn all our friends against me and say i cant control myself. I can never defend myself because she'll say im overeacting and being ridiculous and that im the one that is really mean to her. She always tells me that i need to open up and be myself, but when i do she says that im trying to be just like her, WHEN IM NOT!! I would never wanna be like her. One of the worst things she did to me is when i liked this boy a lot, and she talks to him and one day he called her up and said that he liked HER a lot, she didnt tell me about for days, i didnt have a problem with that, but what she did was say, "OH I KNOW YOU SO WANNA KNOW MY SECRET, IT WOULD MAKE YOU SO JEALOUS". A real friend would apologize and say that the boy liked her and not me, and try to be supportive, not rub it in my face and say how jealous i would be, knowing that i would end up heart broken.Please help, honestly i still want to be her friend because she can be fun to be around, but she can also be really cruel and make me have low self esteem and feel bad about myself, but how can i stay her friend and deal with this, i cant talk to her, ive tried that thousands of times and she said that im overeacting and need to get over it, and then tells me to apologize to her for being so mean, how can i deal with her!? PLEASE HELP!