bad-ass n.

c. 1300, "inadequate, unsatisfactory, worthless; unfortunate;" late 14c., "wicked, evil, vicious; counterfeit;" from 13c. in surnames (William Badde, Petri Badde, Asketinus Baddecheese, Rads Badinteheved). Rare before 1400, and evil was more common until c. 1700 as the ordinary antithesis of good. It has no apparent relatives in other languages.* It is possibly from Old English derogatory term bæddel and its diminutive bædling "effeminate man, hermaphrodite, pederast," which probably are related to bædan "to defile."

The orig. word, AS. bæddel, ME. baddel, on account of its sinister import, is scarcely found in literature, but, like other words of similar sense, it prob. flourished in vulgar speech as an indefinite term of abuse, and at length, divested of its original meaning, emerged in literary use as a mere adj., badde, equiv. to the older evil. [Century Dictionary, 1897]

Comparable words in the other Indo-European languages tend to have grown from descriptions of specific qualities, such as "ugly," "defective," "weak," "faithless," "impudent," "crooked," "filthy" (such as Greek kakos, probably from the word for "excrement;" Russian plochoj, related to Old Church Slavonic plachu "wavering, timid;" Persian gast, Old Persian gasta-, related to gand "stench;" German schlecht, originally "level, straight, smooth," whence "simple, ordinary," then "bad").

Comparative and superlative forms badder, baddest were common 14c.-18c. and used as recently as Defoe (but not by Shakespeare), but yielded to comparative worse and superlative worst (which had belonged to evil and ill).

The meaning "uncomfortable, sorry" is 1839, American English colloquial. To go bad "putrefy" is from 1884. Not bad "fairly good" is by 1771. Ironic use as a word of approval is said to be at least since 1890s orally, originally in African-American vernacular, emerging in print 1928 in a jazz context. It might have emerged from the ambivalence of expressions like bad nigger, used as a term of reproach by whites, but among blacks sometimes representing one who stood up to injustice. In the U.S. West bad man also had a certain ambivalence:

These are the men who do most of the killing in frontier communities, yet it is a noteworthy fact that the men who are killed generally deserve their fate. [Farmer and Henley, "Slang and Its Analogues"]

*Persian has bad in more or less the same sense as the English word, but this is regarded by linguists as a coincidence. The forms of the words diverge as they are traced back in time (Persian bad comes from Middle Persian vat), and such accidental convergences exist across many languages, given the vast number of words in each and the limited range of sounds humans can make to signify them. Among other coincidental matches with English are Korean mani "many," Chinese pei "pay," Nahuatl (Aztecan) huel "well," Maya hol "hole."

"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]