1520s, native or inhabitant of Parthia (ancient kingdom northeast of Persia in western Asia), from Old Persian Parthava- "Parthian," dialectal variant of the stem Parsa-, source of Persia. Partienes (plural) "Parthians" is attested from c. 1300.
As an adjective, "of or pertaining to the Parthians," by 1580s. The phrase Parthian shot is a figurative reference to their horsemen, who were expert at racing forward, turning, and shooting arrows backward at the moment of retreat. The exact phrase is attested by 1832; the image itself was in use long before (for example Parthian fight, 1630s).
Or, like the Parthian, I shall flying fight ["Cymbeline," Act I, Scene VII]