For a few years now for me it was a bunch of EU IV achievements, mostly because achievements in that game require iron man mode and plenty of players don't do that. These were achievements that were done by 0.8% of players.
Yesterday I got a new one though and made me think of starting this thread as I'd find the responses interesting.
My rarest now is Dawi Dominance (0.4%), for Warhammer 2, and requires completing the Mortal Empires campaign as a Dwarf faction.
What's yours? Which game, what % and what is it awarded for?
You can easily determine this by temporarily setting your Steam profile to show achievements showcase, although I think you need a minimum Steam level of 10?