O. achillis was first described by Delforge from the Sporadic island of Skyros in 2013 and its name refers to Achilles, warrior and hero of the Trojan wars. It is a member of the O. attaviria group of Ophrys.

It is another of the eastern Mediterranean's rarer Ophrys, occurring in small numbers only on the Aegean islands of Kos. Kythnos and Skyros. As with many of its orchid species, this taxons survival on Kos is threatened due to the islands enormous herds of goats, subsistence agriculture and seemingly unrestricted tourist development. It can be found growing in very small populations on most types of dry, calcareous soils, particularly in coastal areas.

O. achillis is reported as extremely similar to O. pelinaea and in the opinion of some authorities is synonymous with that species. It does however demonstrate two characteristics which serve to distinguish it and give reason to believe they are distinct taxons. Firstly it is an early flowerer, commencing in late February and past its best by mid March at a time when O. pelinaea is just appearing. The odd plant (as with those depicted here) will however persist until early April, by which time they will be fading fast and be easily distinguished from their cousins. The second and most compelling difference is that they are believed to employ distinct pollinators, which if true is an important consideration. 

The pictures date from the first week of April and are from the hills to the south of Kos town, in the northeast of the island.