After earning his bachelor's degree at the University of Hawaii, Acoba attended law school at the Northwestern University School of Law, earning a Juris Doctor degree there in 1969.
[2] In 1969, Acoba returned to Honolulu to become a law clerk for Hawaii State Supreme Court Chief Justice William S. Richardson.
In 1970, he left this position to become a special assistant to University of Hawaii President Harlan Cleveland.
In 1980, Governor George Ariyoshi appointed Acoba to the Hawaii State Judiciary as a circuit court judge.
Later, Governor Benjamin J. Cayetano appointed Acoba to the Hawaii State Supreme Court.