This achievement requires that you summon the Eidolen Ark with Princess Garnet in the late game. You will need 80MP to summon Ark. To learn to summon Ark you will need to obtain the Accessory item "Pumice". There are a small number of ways to obtain this item.
The easiest way to do this is to collect two pumice pieces and bring them to Hades, who himself is to the right of the screen in Memoria, when you pass underneath the waterfall and enter the underwater area. You will need to defeat Hades to make use of his services. To obtain the two Pumice pieces you need for Hades to form them together, you can do two of the following three options (although the third option is somewhat redundant, and will be explained why).
You may find a Pumice Piece through Chocographing, that is playing Chocobo Hot & Cold in the overworld. Once your chocobo reaches the final ability where it can fly, return to the Chocobo Lagoon and find a Chocograph with this phrase inscribed upon it ""I think there's a desert nearby, Kupo."". Fly to the east of the Outer Continent and the island you are looking for is here. The loot contains a Pumice Piece.
A second piece can be obtained as a drop for defeating Ark in battle. You will battle Ark in Oeilvert as part of the story. There is a 100% chance of Ark dropping the item when defeated. Bring along ONLY Zidane, Steiner, Freya, and Amarant, and equip all with clear-headed to make the battle less difficult, although it shouldn't be too much trouble.
The third piece can be stolen from the Secret boss Ozma. This is the piece that I called redundant, as in order to successfully keep the item you steal from Ozma, you must defeat Ozma, and by defeating Ozma, you have a 100% chance of obtaining a full Pumice. However, Ozma is a very difficult boss, and obtaining the Pumice from Ozma should only be considered an option if you wish to keep the various pieces as useful accessories.
If you have two pumice pieces and are ready to form them together, go back to Hades with the two pieces and 50,000 gil to synthesize them.
Once you have a Pumice, equip it Garnet and enter battle. Summon Ark, sit back and enjoy the show! (It's a LONG animation).