This achievement can be achieved by playing the DLC "Comrades". In Comrades you make your own character and do missions and at level 5 a certain mission will unlock that will give you this achievement.
*** Spoiler - click to reveal ***The mission is under the "Future" tab and is called Department. In this mission you can play either as Noctis, Ignis, Prompto or Gladiolus, and it's basicly an add to the story. To get this achievement you will have to do this mission with all 4 of the characters, but you can only play with 1 character per run. The moment you complete the last run, this achievement will unlock.