Girls, unlike guys, don't easily forgive when you seriously hurt their feelings. That's why in such a situation, you have to apologize in a way that shows you're truly sorry for your actions. And at times, an ordinary "sorry" it's not just enough to make a girl understand how deeply sorry you are, that's why you have to use some words beyond. 

For instance, the words below will not just show how sorry you are but make her remember the cheerful days you both had together.

(1). Even in your hottest anger, you are still the most wonderful girl in the world to me. Dear, I am sorry for everything, I can't wait to see that your beautiful smile.

(2). I know you are mad at me, please forgive me, my princess. You know how difficult it is to cope without you my world.

(3). Please tell me what I need to do to earn your forgiveness. If you want me to bring you the moon I will, my treasure.