Online Etymology Dictionary

achieve (v.): early 14c., from Old French achever (12c.) "to finish, accomplish, complete," from phrase à chef (venir) "at an end, finished," or Vulgar Latin *accapare, from Late Latin ad caput (venire); both the French and Late Latin phrases meaning literally "to come to a head," from stem of Latin caput "head" (see capitulum).
The Lat. caput, towards the end of the Empire, and in Merov[ingian] times, took the sense of an end, whence the phrase ad caput venire, in the sense of to come to an end .... Venire ad caput naturally produced the Fr. phrase venir à chef = venir à bout. ... From this chief, O.Fr. form of chef (q.v.) in sense of term, end, comes the Fr. compd. achever = venir à chef, to end, finish. [Auguste Brachet, "An Etymological Dictionary of the French Language," transl. G.W. Kitchin, Oxford, 1878]
Related: Achieved; achieving.
over-achiever (n.): also overachiever, 1953, from over- + agent noun of achieve (v.). Related: Over-achieve; over-achieving.
achievement (n.): late 15c., "act of completing" (something), from Middle French achèvement "a finishing," noun of action from Old French achever "to finish, accomplish" (see achieve). Meaning "thing achieved" is recorded from 1590s.
under-achiever (n.): also underachiever, 1953, from under + agent noun from achieve (v.). Under-achievement is recorded from 1951.
reprieve (v.): 1570s, reprive, "take back to prison," alteration (perhaps by influence of reprove) of Middle English repryen "to remand, detain" (late 15c.), probably from Middle French repris, past participle of reprendre "take back" (see reprise). Meaning "to suspend an impending execution" is recorded from 1590s; this sense evolved because being sent back to prison was the alternative to being executed. Spelling with -ie- is from 1640s, perhaps by analogy of achieve, etc. Related: Reprieved; reprieving.
mischief (n.): c. 1300, "evil condition, misfortune, need, want," from Old French meschief "misfortune, harm, trouble; annoyance, vexation" (12c., Modern French méchef), verbal noun from meschever "come or bring to grief, be unfortunate" (opposite of achieve), from mes- "badly" (see mis- (2)) + chever "happen, come to a head," from Vulgar Latin *capare "head," from Latin caput "head" (see capitulum). Meaning "harm or evil considered as the work of some agent or due to some cause" is from late 15c. Sense of "playful malice" first recorded 1784.

Mischief Night in 19c. England was the eve of May Day and of Nov. 5, both major holidays, and perhaps the original point was pilfering for the next day's celebration and bonfire; but in Yorkshire, Scotland, and Ireland the night was Halloween. The useful Middle English verb mischieve (early 14c.) has, for some reason, fallen from currency.
effectuate (v.): "bring to pass, accomplish, achieve," 1570s, from French effectuer, from Latin effectus "an effecting, accomplishment, performance" (see effect (n.)). According to OED, formed "on the model of" actuate. Related: Effectuated; effectuating.
rocks (n.): plural of rock (n.1). Meaning "ice cubes" is from 1946; slang meaning "testicles" is first recorded in phrase get (one's) rocks off "achieve intense satisfaction." On the rocks "ruined" is from 1889, figurative use of the expression with reference to ships (by 1735).
last (v.): "endure, go on existing," from Old English læstan "to continue, endure," earlier "follow (a leader), accomplish, carry out, perform," from Proto-Germanic *laistjan "to follow a track" (source also of Gothic laistjan "to follow after," Old Frisian lasta "to fulfill, to pay (duties)," German leisten "to perform, achieve, afford"), from PIE *leis- (1) "track, furrow" (see learn). Related to last (n.1), not to last (adj.). Related: Lasted; lasting.
place (v.): mid-15c., "to determine the position of;" also "to put (something somewhere)," from place (n.). In the horse racing sense of "to achieve a certain position" (usually in the top three finishers; in U.S., specifically second place) it is first attested 1924, from earlier meaning "to state the position of" (among the first three finishers), 1826. Related: Placed; placing. To take place "to happen, be accomplished" (mid-15c., earlier have place, late 14c.), translates French avoir lieu.
exploit (v.): c. 1400, espleiten, esploiten "to accomplish, achieve, fulfill," from Old French esploitier, espleiter "carry out, perform, accomplish," from esploit (see exploit (n.)). The sense of "use selfishly" first recorded 1838, from a sense development in French perhaps from use of the word with reference to mines, etc. (compare exploitation). Related: Exploited; exploiting.
score (v.): "to cut with incisions or notches," c. 1400; "to record by means of notches" (late 14c.); see score (n.). Meanings "to keep record of the scores in a game, etc." and "to make or add a point for one's side in a game, etc." both attested from 1742. The slang sense, in reference to men, "achieve intercourse" first recorded 1960. Meaning "to be scorekeeper, to keep the score in a game or contest" is from 1846. In the musical sense from 1839. Related: Scored; scoring.
rack (v.): "to stretch out for drying," also "to torture on the rack," early 15c., from rack (n.1). Of other pains from 1580s. Figurative sense of "to torment" is from c. 1600. Meaning "raise above a fair level" (of rent, etc.) is from 1550s. Meaning "fit with racks" is from 1580s. Teenager slang meaning "to sleep" is from 1960s (rack (n.) was Navy slang for "bed" in 1940s). Related: Racked; racking. Rack up "register, accumulate, achieve" is first attested 1943 (in "Billboard"), probably from method of keeping score in pool halls.
josh (v.): "to make fun of, to banter," 1845 (intransitive), 1852 (transitive), American English; according to "Dictionary of American Slang," the earliest example is capitalized, hence it is probably from the familiar version of the proper name Joshua. Perhaps it was taken as a typical name of an old farmer.

If those dates are correct, the word was in use earlier than the career of U.S. humorist Josh Billings, pseudonym of Henry Wheeler Shaw (1818-1885), who did not begin to write and lecture until 1860; but his popularity after 1869 may have influence that of the word, or even re-coined it, as it does not seem to have been much in print before 1875.
About the most originality that any writer can hope to achieve honestly is to steal with good judgment. ["Josh Billings"]
Related: Joshed; joshing.
authentic (adj.): mid-14c., "authoritative," from Old French autentique (13c., Modern French authentique) "authentic; canonical," and directly from Medieval Latin authenticus, from Greek authentikos "original, genuine, principal," from authentes "one acting on one's own authority," from autos "self" (see auto-) + hentes "doer, being," from PIE *sene- "to accomplish, achieve." Sense of "entitled to acceptance as factual" is first recorded mid-14c.

Traditionally in modern use, authentic implies that the contents of the thing in question correspond to the facts and are not fictitious; genuine implies that the reputed author is the real one; but this is not always maintained: "The distinction which the 18th c. apologists attempted to establish between genuine and authentic ... does not agree well with the etymology of the latter word, and is not now recognized" [OED].