The Correction of Military Records- to include discharge upgrade goes through the the Secretary of each individual service (Army, Navy, Air Force, Coast Guard). The Board of Corrections (BCMR) and Discharge Review Board (DRB) are both directly run by the Secretary, who has the ultimate authority.
A discharge upgrade requires several elements. 1) The best way to correct your record is to find a procedural defect in the process. 2) The second way is to look at whether or not the discharge or adverse information was equitable (Fair) at the time. 3) The final analysis is whether or not it has served it’s purpose now.