You are suffering damages as the result of someone else's fault. If that party is unwilling to take responsibility you will need to sue her. As you likely aware, the condominium association’s insurance might cover the common areas, but does not cover your particular unit (which is generally defined as the walls or drywall inward). You need to assess the damages caused to your unit, which are generally the cost of repair and potentially loss of use and tally those up. You should also at least notify your insurance carrier to have them define the coverage and deductible.
Beyond those initial steps, you should get an attorney to write a demand letter to your neighbor seeking the costs to repair. She may have insurance of her own that may cover the costs of repair to your unit.
There are numerous attorneys out there that would offer a free consultation to review the matter.
From the limited facts you have disclosed, it appears as if you would likely have a claim against the upstairs neighbor under theories of nuisance or trespass. You may also want to review the terms of your condo declaration for other possible rights. You should consult with an experienced real estate attorney, who will probably advise you to send a demand letter first, then resort to a lawsuit only as a last resort. If your tenant has separate damages and/or has to move out of the unit for a period of time, they should be entitled to recover as well. Make sure you have your condo inspected by a mold remediation company, to ensure that everything is dried out so you won't have other problems down the line.
From what you have written, it sure seems as though you have a valid claim against the upstairs neighbor. Even though she "won't take responsibilities", there may be somewhere in the fine print of the condo contracts a clause mandating that unit owners have liability for any harm to other units that work in their own unit causes. Unfortunately, if she won't voluntarily compensate you, you may have to sue. Consult a local attorney who can consider the facts and situation more deeply, and then give you specific advise.
(THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.)
Water damage in a condominium is one of the most complex problems to address. The result can vary depending on your state law, your condominium documents, your Association's master insurance policy coverage and the facts of the case. First, you or an attorney should review the applicable state law and the condominium documents. In many condominiums the Association's master policy would cover the losses to your unit and your own coverage (HO-6) need only cover your furnishings, wallpaper, etc. Second, your documents could make you or your upstairs neighbor responsible for the deductible on the Association's policy. Third, if your upstairs neighbor was indeed negligent, most condominium documents would allow the Association to assess any damages not covered by insurance against that unit owner--who in turn could make a claim under her insurance policy. I suggest that you contact your condominium's manager and request that the condominium's attorney determine how to cover the losses and reimburse you. That attorney may need assistance from an attorney specializing in insurance coverage claims--most association attorneys do not have that expertise. If the Association does not work with you to resolve the problem, you may need your own attorney to pursue the claim with both the Association and the upstairs unit owner.