To check your rank as as a treasure hunter you have to enter Daguerreo, which is located on an island plateau south of the Forgotten Continent and only accessible once you have the airship or a Gold Chocobo. Once inside the first main area turn right and enter the next room. Activate the lift to get to the top of the room and speak to the Four-Armed Man. He will tell you your Treasure Hunter Rank, which is determined by how many treasure chests, field icons, key items (from sidequests or the Treno Auction House), or Chocograph chests you've discovered. The lowest Treasure Hunter Rank is F and it increases with the more points you accumulate until you reach the highest rank possible, Rank S.
To reach Rank S, you need to accumulate a total of 340 points. A treasure chest and field icon is worth one point and a chest uncovered on Choco (Chocograph chests or ocean bubbles or mountain crack chests) are worth two points each. There are 32 Choco treasures to discover so that is 64 points in total alone and you will earn these on the way to both the Beach Bum and Diggin' It trophies.
You do not need to collect every treasure to reach Rank S and there are enough treasures in the game that you can reach Rank S rather easily. In fact, it's entirely possible to have accumulated enough points to obtain Rank S the first time you can access Daguerreo on Disc 3.
However, if you do miss a fair amount of treasures, many locations in Disc 4 become inaccessible and so you will be left running around looking for the few you missed in fewer locations. Therefore, it's best to collect as many treasures from every location you enter and be as thorough as possible in your search.
Once you’ve reached Rank S, return to the Four-Armed Man in Daguerreo. He will now be sitting on the floor on the bottom of the room he has always been in. He will be shocked that you've reached Rank S and will run away. Find him again at the entrance of Daguerreo and he will identify himself as Gilgamesh and will reward you with the Rank S Reward. You will then obtain this trophy.