When you've finished your first playthrough, choose 'Load Game' and start New Game+. You will know you have been successful if the prologue is skipped in the beginning. This doesn't have to be done in NG+, but it is highly recommended as the game will be much easier this time around. All of your stats and equipment will be available to you, the map locations will remain discovered, and port crystals can now be purchased making travel a thing of the past. You can also access the Ur-Dragon at any time via the port crystal at the beach in Cassardis. At the beginning of NG+ you can also change the appearance of your Arisen and Pawn.
This achievement will unlock after the final credits of your second playthrough.