Cornelius was born in Limerick, Ireland, and it is not clear how he came to be in the United States but he did enlist in the US Army and deployed to the Philippines with Company A, 36th Infantry, US Volunteers. It was his actions with James Gillenwater on the 3rd of September 1889, as a Private that would later earn him the Medal of Honor. The citation reads:

Distinguished gallantry in action in driving off a superior force and with the assistance of 1 comrade brought from the field of action the bodies of 2 comrades, 1 killed and the other severely wounded, this while on a scout.

Cornelius unfortunately did not live to receive the Medal of Honor in person like James did. He was killed in action almost a year later on the 1st of December 1900 near the town of Pilar. Cornelius J Leahy received the Medal of Honor posthumously on the 3rd of May 1902 and he is buried in the San Francisco National Cemetery: Section NA, Site 970.