With Mera's advice of getting Orm from his element (the seas) into his own (a surficial area), Arthur lured Orm into the water surface and dueled him on a warship floating on the water surface, thus forcing him to fight on land, what he is rather unskilled at.
This allowed Arthur to defeat him with a relative ease. Orm than insisted that Arthur would keep the Atlantean tradition of a duel to the death, but Arthur refused and spared Orm's life. When Orm continued to insist, Atlanna showed up and calmed Orm down.
Realizing that even their mother is siding with Arthur, Orm fully surrendered and Arthur was crowned as the king of the United Atlantis.