Just a word of advise for those looking to snag this. Pillars of the community bring down the meter the fastest, although killing off lower civilians works just the same. In order for the district to fully be considered hostile though you need to get the newspaper article on the fall of that particular district. You can simply rest enough days in a row for the people to die of their ailments--that works just fine.
I suggest pairing this with collecting all of the weapons / collectibles so that you can clear out a district, kill off civilians, and then turn it hostile by resting in the end. This also works great when going for:
A few tips from AgentOfAbyss:
1. You MUST deal will all pillars. Mine finally popped after dealing with the final one (Hospital). Embracing them is best of course.
2. The color in the menu changes once the game recognizes a district as hostile. Again I had the hospital at 35%, but the color didn't change until I dealt the the pillar and slept. I did not get all newspapers, but once all four colors greyed out I popped the achievement.
3. Sleeping multiple days in a row without killing anyone doesn't do much. Just kill everyone and then sleep once.
Other TA users claim to have unlocked the achievement without dealing with all pillars.