There's a guide somewhere I read which I followed that got the trophy for me.
Basically you want to
1. Have 9 settlers
2. Build 7 Clinics, assign 7 settlers to them
3. Plant 10 mutfruit, assign 2 settlers to them
4. Have defence of around 60, I used 4 missile turrets at 15 defence each
5. Provide enough beds and water to keep settlers happy
6. Build as many wooden crates as you need to turn your size bar (top right corner in build mode) yellow
Now you basically wait in your settlement for the happiness to go up, once it does, sleep for 24 hours then wait again for it to go up (it can take around 2-3 in game hours. Repeat this process until you reach 100 happiness. It can take a while, at least an hour of real time. NOTE Don't leave your settlement while doing this as it can automatically lower your happiness (glitch)
You may wish to save beforehand, then reload once you have the trophy.