What steps should I take to recieve full payment for damages to my truck?

Last week I was backing out of a parking spot, I made it all the way out and was putting my vehicle in drive when the person behind me backed into the drivers side back end, causing $2000 in damages to my truck. We exchanged information and now her insurance company is telling me that the girl told them we were backing up at the same time and they are saying that they will only pay half. I am just not sure what to do next I do not have collision and would have to pay the other half out of pocket . Any advise would help, I live in Missouri .