Mosquito Swatter is a Feat of Strength Achievement. I happened to earn it while playing my hard core Barbarian in a Torment II Nephalem Rift during Season 4 of Diablo III. Like many things in Diablo III, the ability to earn this Achievement depends on randomness.
When the Rift Boss appeared, it happened to be one named Josh Mosqueira – Reaper Of ‘Soles.
This Rift Boss is named after the Josh Mosqueira who is a Game Director for Diablo III. Players have to kill him to earn the Mosquito Swatter Achievement.