My friend betrayed me and it's obvious she did wrong but she won't apologize for it. She just keeps saying, "How many times do you want me to say I'm sorry!" but she hasn't really said she's sorry.
Learning how to apologize the right way seems to be a lost art. Your friend has given a common response in complaining about having to apologize without actually taking the next step and apologizing.
The right apology includes the words "I'm sorry." It's more than just a small detail, because in order to fully apologize you need to acknowledge that you did something wrong and take responsibility for it.
Saying "How many times should I apologize!" when you haven't apologized at all typically means that someone knows they did wrong but can't admit it. A good way to respond to something like this is to say:
I just want you to apologize once. You haven't yet said you're sorry. Please, just listen to what I'm saying."
You may never get an apology from your friend, so you can either decide to forgive them anyway, or move on from the friendship. The right next step depends on what your friend did and how much you want to keep the friendship.
One response you could use would be:
"I care about your friendship, and I don't want this latest incident to end things for us. You did hurt me, and despite complaining about having to apologize, you still haven't done it. It would mean a lot to me just to hear you say "you're sorry," but I can see you're not going to do that. I want you to know I forgive you, but I'd like our friendship to be better than this. The next time something happens, please just say you're sorry."
Your friend may eventually learn that the right apology at the proper time can help both of you move on more quickly from conflict.