The 1985 half penny is one of the scarcest years for the denomination. It is scarce, I wouldn't label it as rare. The coins had a short period in circulation, and relatively small quantity have survived Irish Coinage
is the best place for info on Irish coins.
I have no idead of what its market value would be currently, but I wouldn't pay more than 20 Euro for one. You never know when a bag of them will turn up!