gun-slinger n.

mid-14c., gunne "an engine of war that throws rocks, arrows or other missiles from a tube by the force of explosive powder or other substance," apparently a shortening of woman's name Gunilda, found in Middle English gonnilde "cannon" and in an Anglo-Latin reference to a specific gun from a 1330 munitions inventory of Windsor Castle ("... una magna balista de cornu quae Domina Gunilda ..."). Also compare gonnilde gnoste "spark or flame used to fire a cannon" (early 14c.).

The woman's name is from Old Norse Gunnhildr, a compound of gunnr and hildr, both meaning "war, battle." First element from PIE *gwhen- "to strike, kill" (see bane); for second, see Hilda.

The identification of women with powerful weapons is common historically (such as Big Bertha, Brown Bess, Mons Meg, etc.).

Or perhaps gun is directly from Old Norse gunnr "battle." The word was perhaps influenced by or confirmed by (or possibly from) Old French engon, dialectal variant of engin "engine."

Meaning grew with technology, from cannons to firearms as they developed 15c.; popularly applied to pistols and revolvers from 1744. In modern military use the word is restricted to cannons (which must be mounted), especially long ones used for high velocity and long trajectory. Hence great guns (1884 as an exclamation) distinguished from small guns (such as muskets) from c. 1400. Meaning "thief, rascal" is from 1858. For son of a gun, see son. To jump the gun (1912, American English) is a figurative use from track and field. Guns "a woman's breasts" (especially if prominent) attested by 2006.

[G]un covers firearms from the heaviest naval or siege guns (but in technical use excluding mortars and howitzers) to the soldier's rifle or the sportsman's shotgun, and in current U.S. use even the gangster's revolver. In the other European languages there is no such comprehensive word, but different terms for the small or hand gun of the soldier or sportsman (even these, sometimes differentiated) and the heavy naval guns or artillery pieces .... [Buck, 1949]

c. 1300, "hand-held implement for throwing stones" (consisting of a strap and two strings), from an unidentified continental Germanic source (such as Middle Low German slinge "a sling") from verbs meaning "swing to and fro, wind, twist" (see sling (v.1)).

The notion probably is of being twisted and twirled before it is released. The piece of stone or metal hurled from it is a sling-stone (late 14c.). The older English word for this ancient weapon was lithere (Old English liþere, related to leather).

Some of the sense developments might have been influenced by Low German cognates. The sense of "loop for lifting or carrying heavy objects" is recorded by early 14c. As "leather shoulder strap for a rifle, etc.," by 1711. The meaning "piece of cloth tied in a hanging loop around the neck to support an injured arm" is attested by 1720. A Middle English medical word for "sling or supporting loop used in treating dislocations" was stremb (early 15c., Chauliac, who also has suspensorie), from Medieval Latin stremba. 

The Greeks, Romans, and Carthaginians had bodies of slingers attached to their armies, recruited especially from the inhabitants of the Balearic Isles. The use of the sling continued among European armies to the sixteenth century, at which time it was employed to hurl grenades. [Century Dictionary]