The answer to the question 'can i get my girlfriend back?' is yes... probably. You see if your girl still loves you, no matter how much you've messed up in the past, she will more than likely be receptive to you if you can prove to her that she won't be wasting her time and that she won't get hurt again. No one wants to be hurt and no one wants to set themselves up to be hurt by trusting someone who has already proven they can't be trusted. For this reason you will probably be able to win her back but you had better expect an uphill climb.
The first step is to give her a little time and space. Don't rush her or expect everything to happen quickly. It takes a lot longer to rebuild trust than it took to tear it apart. More than likely by the time you've gotten to this point you've let her down more than once. Please don't think that all that past hurt and all those mistakes will go away and she'll forget about them just because you say 'I'm sorry' or you tell her that 'I've changed'. She'll probably need to see some proof that that is true.
It's important for you to concentrate on yourself instead of just trying to convince her you've changed. It will take you time to truly change the person that you are and you don't want to make the mistake of thinking you can somehow 'trick' her into believing you are a different man.
It's true, you may be able to but what will that accomplish? Eventually she'll just see that you've lied to her... again and she'll just leave you all over again. Eventually she won't fall for it and the two of you will truly be done. Much better to actually make the changes and make them permanently. It will not only give you the answer to the question 'can i get my girlfriend back' it will also help you to keep the relationship strong and just make you a better man overall.
Depending on how much time has passed since the two of you broke up, you may want to start all over with her. Pretend like the two of you are just getting to know each other. Take it very slow. The worst thing you can do at that point is to try and talk her into trusting you again. This is just more lip service. Instead try to spend time with her, just as a friend, and let her see that you've really changed. When she sees it with her own eyes it's much more likely that she'll learn to trust you again.
Remember, if you want to know 'can i get my girlfriend back?' the answer really lies mostly with you. Love doesn't die that easily so unless you really treated her badly it's very likely that she still cares for you. It's up to you to prove to her that she's not a fool for it.