This is the last achievement in the Railroad questline (excluding The Nuclear Option, which can also be achieved siding with the Minutemen or the Brotherhood).
While the other solution is helpful, it is rather chaotic, so I wanted to share a chart I made with the way of getting all the story achievements with only one save / reload
, and also the best point to save in order to obtain all 4 endings (not necessary for achievements).
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!