potshot n.

"deep, circular vessel," from late Old English pott and Old French pot "pot, container, mortar" (also in erotic senses), both from a general Low Germanic (Old Frisian pott, Middle Dutch pot) and Romanic word from Vulgar Latin *pottus, which is of uncertain origin, said by Barnhart and OED to be unconnected to Late Latin potus "drinking cup." Similar Celtic words are said to be borrowed from English and French.

Specifically as a drinking vessel from Middle English. Slang meaning "large sum of money staked on a bet" is attested from 1823; that of "aggregate stakes in a card game" is from 1847, American English.

Pot roast "meat (generally beef) cooked in a pot with little water and allowed to become brown, as if roasted," is from 1881. Pot-plant is by 1816 as "plant grown in a pot." The phrase go to pot "be ruined or wasted" (16c.) suggests cooking, perhaps meat cut up for the pot. In phrases, the pot calls the kettle black-arse (said of one who blames another for what he himself is also guilty of) is from c. 1700; shit or get off the pot is traced by Partridge to Canadian armed forces in World War II. To keep the pot boiling "provide the necessities of life" is from 1650s.

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 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"]