hard-ass adj.

Old English heard "solid and firm, not soft," also, "difficult to endure, carried on with great exertion," also, of persons, "severe, rigorous, harsh, cruel," from Proto-Germanic *hardu- (source also of Old Saxon hard, Old Frisian herd, Dutch hard, Old Norse harðr "hard," Old High German harto "extremely, very," German hart, Gothic hardus "hard"), from PIE *kortu-, suffixed form of root *kar- "hard."

Meaning "difficult to do" is from c. 1200. Of water, in reference to the presence of mineral salts, 1650s; of consonants, 1775. Hard of hearing preserves obsolete Middle English sense of "having difficulty in doing something." In the sense "strong, spiritous, fermented" from 1789 (as in hard cider, etc.), and this use probably is the origin of that in hard drugs (1955). Hard facts is from 1853; hard news in journalism is from 1918. Hard copy (as opposed to computer record) is from 1964; hard disk is from 1978; the computer hard drive is from 1983. Hard times "period of poverty" is from 1705. Hard money (1706) is specie, silver or gold coin, as opposed to paper. Hence 19c. U.S. hard (n.) "one who advocates the use of metallic money as the national currency" (1844). To play hard to get is from 1945. Hard rock as a pop music style recorded from 1967. To do something the hard way is from 1907.

"backside," attested by 1860 in nautical slang, in popular use from 1930; chiefly U.S.; from dialectal variant pronunciation of arse (q.v.). The loss of -r- before -s- is not uncommon (burst/bust, curse/cuss, horse/hoss, barse/bass, garsh/gash, parcel/passel).

Indirect evidence of the change from arse to ass can be traced to 17c. By 1680s arse was being pronounced to rhyme with "-ass" words, as in "Sodom or the Quintessence of Debauchery": "I would advise you, sir, to make a pass/Once more at Pockenello's loyal arse." It is perhaps as early as Shakespeare's day, if Nick Bottom transformed into a donkey in "A Midsummer Night's Dream" (1594) is the word-play some think it is.

I must to the barber's, mounsieur; for me thinks I am marvellous hairy about the face; and I am such a tender ass, if my hair do but tickle me, I must scratch. [Bottom]

By 1785 polite speakers were avoiding ass in the "donkey" sense. 

The meaning "woman regarded as a sexual object" is by early 1940s (piece of ass seems to be implied in 1930s Tijuana Bibles), but the image is older (compare buttock "a common strumpet," 1670s). To have (one's) head up (one's) ass "not know what one is doing" is attested by 1969. Colloquial (one's) ass "one's self, one's person" attested by 1958. To work (one's) ass off "work very much" is by 1946; to laugh (one's) ass off "laugh very much" is by 1972 (implied from 1965). The (stick it) up your ass oath is attested by 1953; apparent euphemisms suggest earlier use:

He snoighed up his nose as if th' cheese stunk, eyed me wi an air o contempt fro my shoon to my yed, un deawn ogen fro my yed to my shoon ; un then pushin th' brade un cheese into my hont ogen, he says "Take your vile bread and cheese and stick it up your coat sleeve, and be demmed to you. Do you think I want your paltry grub?" Un then, turnin on his heel, he hurried into th' perk. ["Bobby Shuttle un His Woife Sayroh's Visit to Manchester," 1857]