You should file a police report and contact a local attorney
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Do file a police report. This is criminal damage. As far as your options from there, file an insurance claim with your insurer. After that, it is for the ensurer to pursue her. Everything else is probably over-kill for the amount of damages. If you do not have insurance, you could sue her. You can get her address from MVD using her license plate number.
But if you do want to pursue it, to prove you did not hit her, check with the stores and property management to see if there is parking lot security and store security tapes. They recycle these tapes, so you need to act quick to get copies. Even if there is no parking lot security, if you can get a tape of when she entered a store, you can circumstantially prove when she parked. You will also want to prove when you parked, so get security tapes for the store(s) you were in. Also, keep your receipts, because these are likely date and time stamped--and if not, the store computer should be able to print out the time and date of the sale. You will also use her statement that either another car hit you before she got there, or you pulled too far forward and hit her. By saying another car hit you before she got there, she almost admits you were there first--in which case you did not pull forward and hit her because you were already parked when she got there. Also, if you hit her, she would have been a lot more concerned about her car. The fact that she was unconcerned about her own car helps show that she does not really believe you hit her.
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You can use the plate information determine who the person is and send them a letter stating you are making a claim for the damage. You may also get a phone number that will allow you to call her. If she will not cooperate, you will either need to go through your insurance and they can go after her on a "subrogation" claim or you will need to sue her yourself, possibly in small claims court.
You can make a property damage claim under the other driver's insurance. You need to report the incident to the police. The police likely won't issue an accident report because the accident happened on private property. However, you can request that the police generate an incident report number for you. By both reporting the accident to the police and having an incident report number generated, it will help when setting up a claim with the insurance company for your property damage. You may also be able to make a claim under your own insurance depending on your coverage or pursue the other driver personally if they have no insurance. It's always best to speak with counsel to review all your legal options.