Not much detail with regards to which item this was or how UPS "destroyed it" or any interaction you have had with the buyer. As tobaccocardyahoo noted if you purchased your UPS label through eBay you cannot file a claim with UPS, eBay has to do that and what are the odds of that happening.
As with USPS either the shipper or the receiver can file a claim with the carrier and it is often easier for the receiver to do so since the carrier often wants the damaged item and the original packing to be brought into a local store/PO for inspection.
Damage claims are often tough to handle and the biggest hurdle I have ran into is where I cannot get any assistance/cooperation from the buyer on trying to resolve the claim. I seldom use UPS but the one damage claim I had several years ago took time and a lot of effort, more than should have been required, to resolve. Fortunately I had a great buyer who was more than willing to assist in getting it resolved. As a side not this label was not bought through eBay.
