sharp-shooter n.

Old English scearp "having a cutting edge; pointed; intellectually acute, active, shrewd; keen (of senses); severe; biting, bitter (of tastes)," from Proto-Germanic *skarpaz, literally "cutting" (source also of Old Saxon scarp, Old Norse skarpr, Old Frisian skerp, Dutch scherp, German scharf "sharp"), from PIE root *sker- (1) "to cut" (source also of Lettish skarbs "sharp," Middle Irish cerb "cutting").

The figurative meaning "acute or penetrating in intellect or perception" was in Old English; hence "keenly alive to one's own interests, quick to take advantage" (1690s). Of words or talk, "cutting, sarcastic," from early 13c. Meaning "distinct in contour" is from 1670s. The musical meaning "half step above (a given tone)" is from 1570s. Meaning "stylish" is from 1944, hepster slang, from earlier general slang sense of "excellent" (1940). Phrase sharp as a tack first recorded 1912 (sharp as a needle has been around since Old English). Sharp-shinned attested from 1704 of persons, 1813 of hawks.

Middle English sheten "hasten from place to place; move swiftly; thrust forward; discharge a missile, send an arrow from a bow," from Old English sceotan (class II strong verb; past tense sceat, past participle scoten), "dart forth, go swiftly and suddenly," also "discharge (a missile or weapon);" also, of a person, "go suddenly from place to place;" also transitive "send out or forth with sudden or violent motion; put forth or extend in any direction; strike with anything shot."

This is from Proto-Germanic *skeutanan (source also of Old Saxon skiotan, Old Norse skjota "to shoot with (a weapon); shoot, launch, push, shove quickly," Old Frisian skiata, Middle Dutch skieten, Dutch schieten, Old High German skiozan, German schießen), often said to be from PIE root *skeud- "to shoot, chase, throw," but Boutkan gives it no IE etymology.

The sense of "dart along" (as pain through the nerves or a meteor in the sky) is by late 13c.; that of "come forth" (as a plant) is by late 15c. As "increase rapidly, grow quickly" by 1530s (often with up (adv.)). By 1690s as "be emitted in rays or flashes" (as light is); by 1530s in weaving, "variegate by interspersing colors."

The general sports sense of "kick, hit, throw etc. toward the goal" is by 1874. In reference to pool playing, by 1926. The meaning "strive (for)" is by 1967, American English. The sense of "descend (a river) quickly" is from 1610s. The slang meaning "to inject by means of a hypodermic needle" is attested by 1914 among addicts. The meaning "to photograph" (especially a movie) is from 1890.

As an interjection, an arbitrary euphemistic alteration of shit, it is recorded by 1934.

Shoot the breeze "chat" is attested by 1938 (as shooting the breeze), perhaps originally U.S. military slang. Shoot to kill is attested from 1867. Slang shoot the cat "vomit" is from 1785.

To shoot the moon formerly meant "depart by night with ones goods to escape back rent" (c. 1823).

O, 'tis cash makes such crowds to the gin shops roam,

And 'tis cash often causes a rumpus at home ;

'Tis when short of cash people oft shoot the moon ;

And 'tis cash always keeps our pipes in tune.

Cash! cash! &c.

["The Melodist and Mirthful Olio, An Elegant Collection of the Most Popular Songs," vol. IV, London, 1829]

Shoot against the moon was used by Massinger  (1634) as a figure of an impossible attempt.