Origin and history of upshot

Middle English shot "a missile, arrow, dart" (senses now archaic or obsolete); "a swift movement, a gushing out," from Old English scot, sceot "a shot, a shooting, an act of shooting; that which is discharged in shooting, what is shot forth; darting, rapid motion."

This is reconstructed to be from Proto-Germanic *skutan (source also of Old Norse skutr, Old Frisian skete, Middle Dutch scote, German Schuß "a shot"), from PIE root *skeud- "to shoot, chase, throw." The Old English noun is related to sceotan "to shoot." The meaning "discharge of a bow, missile," also is from related Old English gesceot.

The noun was extended to other projectiles (balls, bullets) by mid-15c. Especially "lead in small pellets, a small ball or pellet," a number of which are combined in one charge, which is attested by 1770 (shortened from earlier small shot, 1727).

The general sense of "an attempt to hit with a projectile" is by 1650s. Extended to sports (hockey, basketball, etc.) by 1772, originally in curling. It is attested by early 15c. as "range or distance of a missile in flight," hence "range" in general (c. 1600), as in earshot. 

Another original meaning, "payment" (perhaps literally "money thrown down") is preserved in scot-free; also see scot (n.). The notion of "throwing down" might have led to the meaning "a drink," first attested 1670s; the more precise meaning "small drink of straight liquor" is by 1928.

The sense of "hypodermic injection" is attested from 1904; the figurative phrase shot in the arm "stimulant" is by 1922. The broad meaning "a try, an attempt" is by 1756; the sense of "remark meant to wound" is by 1841. The meaning "an expert in shooting with a firearm" is from 1780; the sense of "a rocket flight" is by 1934. The camera-view sense is by 1958.

To call the shots "control events, make decisions" is American English, 1922, perhaps from sport shooting. Shot in the dark "uninformed guess, random attempt" is by 1885. Big shot "important person" is from 1861. 

By the rude bridge that arched the flood,

  Their flag to April’s breeze unfurled,

Here once the embattled farmers stood

  And fired the shot heard round the world.

[Emerson, from "Concord Hymn"] 

a prefix bringing various senses of up, including "toward a more elevated position; at or to a source, head, or center; in or to an erect position;" originally from Old English up (adv.). It corresponds to Dutch op-, German auf-, Old Norse upp-.

Modern formations with it include upchuck, update, upfield, upgrade (v.), upload, upswing (n.), upscale, uptight, all from 20c.

The prefix was highly productive in Old and Middle English (and among poets of all eras), forming up-verbs where modern English uses "verb up." Some of these (uplift) survive.

Many do not: Upbear, upblaze, upblow, upbreak, updress, upgive, uphang, upshut, upsit, upspeak, uptie, upthrow, upwake, etc. The old verbs are not so much archaic as dissolved. In a few cases two forms survive to sustain (sometimes contrary) distinct senses: Hold up and uphold; set up and upset.