The Treasure Hunter side quest and Treasure Hunter Rank are part of an optional side quest that completed during a regular playthrough of the game. The reward for completing the quest is obtaining Rank S and the Rank S Award key item.
The Treasure Hunter Rank is determined by the number of hidden treasure chests that you opened, items that you obtained during event sequences and items found on the world map through the Chocobo Hot & Cold side quest.
Travel Daguerreo and speak to the four-armed man to receive the reward.
You will automatically obtain the Another Man’s Treasure Trophy once you have achieved “Rank S”.