Hi, if you have tried to mend things with her, but she is still not reciprocating then I would suggest you to keep trying harder. And once she sees that you truly mean to apologise and change and see it through your actions rather than just your words, then she will come around. Just give it some time, and be persistent with your efforts. Everything would be fine, just put your best foot forward.
The context of your situation is a bit unclear. From what you have shared I understand that you cheated on your partner and even though you have apologized, she cannot bring herself to forgive you.
If that is the case, this may be a test in patience for you and healing for her.
To be cheated on is one of the most painful experiences in a relationship. Recovery from it, while very much possible, is something that takes time.
While it's important that you take responsibility for your actions, you cannot also push her into forgiving you. Doing so may only make her more resentful. So what do you do? Since it is a process, I suggest you seek therapy. If not, you could also refer to the book "why won't you apologize" by Harriet Lerner. It's a very insightful book on hurts and healing from them.
Be prepared that it is not just a matter of the words you use but the process. So be patient.