"sharpshooter; one who shoots from a hidden place," 1824, agent noun from snipe (v.). The birds were considered a challenging target for an expert shooter:
Snipe Shooting is a good trial of the gunner's skill, who often engages in this diversion, without the assistance of a dog of any kind; a steady pointer, however, is a good companion. [Sportsman's Calendar, London, December 1818]
"spaniel dog trained to start woodcock and snipe in woods and marshes," 1811, from cock (n.1).