He was one of the first Europeans to reach and climb the country's second tallest mountain - Mount Giluwe (1934). However, Jack Hides had also laid claim to be the first to discover Mount Giluwe, so Leahy went to England in 1935 and forced the Royal Geographical Society to set up a hearing into the two opposing claims. The following year Leahy was awarded the Murchison Award by the Society and published his discoveries in their journal.