Apparently, around about 1795, a mermaid was, indeed, found on the beach at Greenhill. The transcription of a deposition by a Colin MacNiven makes for a good read.
If I understand this document correctly the deposition was made just prior to the 'mermaid's' remains being exhumed, some 18 years after they had been buried.
As you will see, this document is part of the online archive which can be found at the relatively new An Iodhlann site. On the off-chance that you don't know, An Iodhlann is the historical centre - a museum and archive - here on the Isle of Tiree. Please do visit their wonderful site and, when you visit in person, go along and say 'hello'.