You need to collect the 13 items from the Pirate page in the Museum. 4 of the items are the pirate flag you need to collect for the second quest. 1 item is the pirate treasure you need to collect for the final quest. Make sure you have found all the other pieces before picking up the final chest because when you return to the top of the level it will end. The rest of the items are randomly spread throughout the level (though many are found deeper in the ground).
The achievement will unlock as soon as you pick up the final item. I unlocked this during the campaign play of the Ocean level, collecting all the items in one play through. If for some reason you miss one in campaign play, start a new game in Freeplay mode since your digger is fully upgraded from the beginning and you can drive deep into the map quicker to find your missing item.