You have a huge uphill battle on this one. First you need to leave her alone. Begging wont help. You need to figure a way to be friends with her. Then show her you can be trusted. Odds are you're not getting this girl back.
Instead of focusing on "getting her back" you need to focus on fixing the problems that caused that loss of trust. Then if you two are still around each other, she'll see your improvements and you may get back together. But right now, you need to focus on yourself.