Sergeant Costa was a member of Headquarters Company, 3rd Battalion, 8th Cavalry Regiment, 1st Cavalry Division. He was taken Prisoner of War while fighting the enemy near Unsan, North Korea, on 2 November 1950 and died while a prisoner on 31 March 1951. His remains were not recovered. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Costa was awarded the Purple Heart, the Combat Infantryman's Badge, the Prisoner of War Medal, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.