This achievement is obtained by completing the main storyline following the quests of one of these factions: Minutemen, Railroad or Brotherhood. You only need to do one of these, not all three.
While the other guide is helpful, it is rather chaotic, so I made a chart that shows how to obtain all the achievements with only one save / reload
. My guide shows how to unlock "The Nuclear Option" while aligned with the Brotherhood, but I also indicate when to diverge from these steps, if you want to play the Railroad or Minutemen endings.
Scroll down for a more detailed explanation (inside the Spoiler Tag, as it is an awful lot of text).
For starters, keep in mind a thing: having high charisma
will help you when you'll have to balance several factions at once. I recommend having at least 6-7 points of charisma, and using "charisma-enhancer" gear like Glasses, Hats or Suits, or even using, when neccessary, beer or some drugs as Grape Mentats or Day Tripper that give charisma points for a few minutes.
Open this thing for the full explanation:
Hope it helps!