Some mistakes are too big to recover from. Some boundaries cannot be uncrossed. However, if there’s even a chance she’s going to forgive you for the mistakes you’ve made, you should give her a genuine, heartfelt apology. You should make it clear that you’re never going to hurt her again in the future.
The most important thing you can do is own up to your mistakes. Feel free to explain the reasoning behind why you did what you did, but make sure it doesn’t sound like you’re throwing out random excuses. You shouldn’t pass the blame off to your exes, your parents, your friends, and everyone else around you. You should be mature enough to say I screwed up and I’m sorry. If you can’t even admit what you’ve done wrong — or can’t even see what you’ve done wrong — then she’s not going to give you another chance. The first step is being self-aware.
If you want her to forgive you, then you need to take her feelings seriously. You cannot accuse her of overreacting or act like she doesn’t have a right to be upset with you. You can’t tell her how to feel. You have to respect her emotions and understand that they are just as valid as yours.
If you want her to forgive you, then you need to promise you’re going to treat her better in the future — but you actually have to carry through on that promise. You can’t act like you’re going to turn your attitude around one day and go right back to your old habits the next day. If you keep repeating your mistakes, you might keep her around for the short-term, but she’s going to be gone soon. She’s going to come to her senses and realize you aren’t a man of your word.
If you want her to forgive you, don’t rely on expensive gifts to do the talking for you. If you want to start making things up to her by surprising her with flowers and chocolates, then have fun. However, don’t assume your work is over. You can’t buy her trust back. Your changed behavior is the best apology.
If you want her to forgive you, make sure you actually say what you mean. Say you’re sorry. Say you love her. Say you aren’t going to hurt her again. Don’t assume she already knows those things. Don’t assume your feelings can go without being said. Be clear that you want her, you want this relationship, and you want to be the best partner you can be.
If you want her to forgive you, you have to give her time. You can’t rush her toward healing. It might take her a little while to come to terms with what you’ve done. She probably won’t snap back to hugging and kissing you right away. But if she’s the only one you want, then she’ll be worth the wait.
Just remember, she doesn’t want you to apologize in order to shut her up. She wants you to apologize because you mean it, because you feel horrible about hurting her, because you believe she deserves better. 
