The term probably originated in the 1920s with Captain Cornelius W. Willemse, who "busted" many criminal "gangs."
(Oxford English Dictionary)
gangbuster, n., a., and adv.
colloq. (orig. U.S.)
Popularized by the long-running U.S. radio serial Gang Busters (1936-57).]
1. An officer of a law-enforcement agency who is known for successful (and often aggressive) detection of organized crime.
1930 N.Y. Times Bk. Rev. 7 Dec. 18 Captain Willemse was known as 'the gang buster' because of the part he played in the breaking up of the Kid Dropper, Little Augie and Flanagan gangs.
1940 Common Sense July 9/1 The boys with leather boots who liked to act as a combination of Army, vigilantes, Ku Kluxers, gangsters, gangbusters and defenders of the pure Italian or German way of life.
2. like (the) gangbusters: with great speed, force, or urgency; (hence) vigorously, successfully. Freq. in to come on (also in) like gangbusters. Also occas. as adj.: forceful, vigorous.
1940 Current Hist. & Forum 7 Nov. 21 [In a glossary of prison slang] Coming on like Gang Busters means doing all right.
1942 Z. N. HURSTON in Amer. Mercury July 89 Man, I come on like the Gang Busters, and go off like The March of Time!
7 December 1930, New York (NY) Times, book review, pg. 18:
Captain Cornelius W. Willemse, who served twenty-five years in the New York City Police Department, rising from patrolman to captain of the homicide squad in charge of the First Detective Division, has just finished writing the story of his life. It will be published in February by Alfred A. Knopf under the title "Behind the Green Lights." Captain Willemse was known as "the gang buster" because of the part he played in the breaking up of the Kid Dropper, Little Augie and Flanagan gangs. The book begins with Willemse's arrival in America as an immigrant boy from Holland, carries him through his days on the Bowery as a derelict and saloon "bouncer" and ends with the shooting of Legs Diamond.
8 February 1931, New York (NY) Times, pg. 64:
BEHIND THE GREEN LIGHTS.
By Captain Cornelius W. Willemse. In collaboration with George J. Lemmer and Jack Kofoed. 364 pp. New York: Alfred A. Knopf. $3.
By BRUCE RAE
THE third degree is demonstrated and defended in Captain Willemse's realistic tale of cops and crooks, of the old flamboyant days of the Tenderloin and of the newer rackets and racketeers -- the autobiography of a detective whose twenty-five years of successful work in the New York Police Department earned him the title of the Gang Buster.
12 July 1942, New York (NY) Times, pg. 35:
C. W. WILLEMSE, 70
Former Captain on Force Here,
Who Was Noted for Breaking
Up Gangs, Retired in '25
A WRITER AND LECTURER
"Behind the Green Lights" and
"A Cop Remembers" Dealt
With His Experiences
Cornelius W. Willemse, former captain of detectives, who turned writer, lecturer and restaurateur after his retirement seventeen years ago, died yesterday in St. Clare's Hospital, 415 West Fifty-first Street, after an emergency operation for appendicitis.
Known as Gang-Buster
The police called him the gang-buster, a title he earned by eliminating the Kid Dropper band of the early Twenties and the equally notorious gang led by "Little Augie" Pisano. Kid Dropper himself was killed in front of the Essex Market COurt in August, 1923, after Captain WIllemse had rounded him up.