The most common and most likely answer to this crossword clue is the 4 letter word DONE
I've seen this crossword clue in The Times
D
O
N
E
More clues leading to the result DONE
Buddy explains!

The straight part
We know that "Accomplished" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case accomplished = done.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does DONE mean?
DONE verb- (auxiliary) A syntactic marker.
- To perform; to execute.
- To cause, make (someone) (do something).
- To suffice.
- To be reasonable or acceptable.
- (ditransitive) To have (as an effect).
- To fare, perform (well or poorly).
- (chiefly in questions) To have as one's job.
- To perform the tasks or actions associated with (something).
- To cook.
- To travel in, to tour, to make a circuit of.
- To treat in a certain way.
- To work for or on, by way of caring for, looking after, preparing, cleaning, keeping in order, etc.
- To act or behave in a certain manner; to conduct oneself.
- To spend (time) in jail. (See also do time)
- To impersonate or depict.
- (with 'a' and the name of a person, place, event, etc.) To copy or emulate the actions or behaviour that is associated with the person or thing mentioned.
- To kill.
- To deal with for good and all; to finish up; to undo; to ruin; to do for.
- To punish for a misdemeanor.
- To have sex with. (See also do it)
- To cheat or swindle.
- To convert into a certain form; especially, to translate.
- To finish.
- To work as a domestic servant (with for).
- (auxiliary) Used to form the present progressive of verbs.
- To cash or to advance money for, as a bill or note.
- (ditransitive) To make or provide.
- To injure (one's own body part).
- To take drugs.
- (in the form be doing [somewhere]) To exist with a purpose or for a reason.
- (of food) Ready, fully cooked.
- Having completed or finished an activity.
- Being exhausted or fully spent.
- Without hope or prospect of completion or success.
- Fashionable, socially acceptable, tasteful.
- A synthetic opioid analgesic, used to wean addicts off heroin or other opiate based narcotics, and in chronic pain management.