To earn this achievement you must find all 20 treasures on the 20 islands using the Expedition section in the menu. You can see them on Page 2 with the yellow icon.
Leymon Sea - Red Jeweled Pendant
Diomell Islands - Twin's Clothes
Exsphere Sea - Yggdrasill Goddess Statue
Asras Sea - Fantasic Landscape
Kanonno Island - Portrait of the three guardians
Normin Island - Empyrean Tablet
Soma Volcano - Spira Core Crystal
Barbatos Archipelago - Bone Mask
Force Islands - Antique Tarot Cards
Amarcian Subcontinent - Valkines Cryas Trinket
Crystaliron Sea - Oresoren Brothers
Centurion Isles - Crimson Crystal
Teepo Island - Snow Globe of Growth
Kresnik Island - Glowing Gear
Krityan Island Archipelago - Bodhi Blastia Bracelet
Cheagle Island - Replica Key of Lorelei
Isles of Noc and Dia - Moon and Star Earrings
Albane - Cleric's Staff
Swordian Peninsula - Eye of Atamoni Statue
Quickie Peninsula - Model Craymel Cage