Mostly from Richard Sears' Chinese Etymology site (authorisation), which in turn draws data from various collections of ancient forms of Chinese characters, including:
Derived as aggressive clipping of お疲れ様です(otsukaresama desu, used as a kind of greeting at work, literally “that's honorable exhaustion (from hard work)”). The use of 乙 for the spelling is an example of phoneticateji (当て字).
Cognate with the initial oto- in 劣る(otoru, “to be less than; to be younger than”), 落とす(otosu, “to drop something”).[3][1] Also the first element in 弟(otōto, “younger brother”).
[from late 1500s](archaic,Nohtheater)clipping of 乙御前(oto goze): a stock character in 狂言(kyōgen) comic interludes, played as a plump and clumsy but earnest young woman
From a Late Middle Chinese pronunciation of 乙 (MC 'it), which lenited coda /-t/ to /-r/.[1]
Phonogram
乙 (*-r)
A consonantal phonogram denoting coda consonant *-r
Usage notes
Generally believed to have been pronounced as *-r, based both on internal evidence and the Chinese etymon. Old Korean 尸(*-l) and 乙(*-r) both merged unconditionally into *-l in Middle Korean, but the two phonograms were consistently distinguished in Old Korean until the late thirteenth century. Because Old Korean reconstructions are conventionally romanized using their Middle Korean reflex, the phonologically erroneous reconstruction *-l is often used as a shorthand.
In Middle and Modern Korean, the allomorph taken by the accusative marker after a vowel may be 를 (-reul) instead of ㄹ (-l), especially in formal speech. This is the result of reduplication of the particle and is unlikely to have been present in Old Korean, although the phonologically opaque nature of the orthography makes it difficult to tell for sure.
In "Middle Old Korean", the late first-millennium stage of Korean represented by about a dozen mostly eighth-century poems, the accusative particle was consistently written with the phonogram肹. 乙 has become dominant by the twelve poems of the tenth-century monk Gyunyeo, however, and 肹 is virtually not attested at all by the second millennium. There seems to be no semantic difference involved. Whether this represents a phonetic shift or simply a change in orthographic practice is unknown, although 肹 and 乙 had differing Middle Chinese initials.[2][3]