For the mask obtained from the Clothier, see Mime Mask.
Boss Masks are vanity items dropped by all non-eventbosses, with the exception of the Old One's Army. They are worn in the social head slot. Each boss has a 14.29% chance to drop its own mask.
The Ancient Cultist Mask is arguably the most difficult to obtain, not because it is hard to defeat the Lunatic Cultist, but because it is impossible to farm him without spawning in the Lunar Events. The Events must be completed in order for the Cultists outside of the Dungeon to spawn, which must be killed in order for the Lunatic Cultist to be spawned again. Doing all of it may take a long time, which may make the Mask not worth it.