There are six main quests you need to finish to get this achievement. To start the first one you either have to be ESO Plus subscriber or buy the DLC from the Crown Store. Anytime it fits you, go to the Collections tab and find it under Stories. The quests are:
- The Dragon's Lair
- Reformation
- Uneasy Alliances
- Order of the New Moon
- The Pride of Alkosh
- The Dragonguard
All but one start automatically after the previous one is finished. The exception is the "Uneasy Alliances" quest. To start it talk to the certain creature you meet (hard to miss as it's in front of you). The achievement will pop-up once you finish "The Dragonguard" last dialogue.