Just a little trick - it appears you don't actually need to build every district type to get this achievement, but you do need 12 total. Some districts can't be built ever in a city, for example, if you don't settle your city near a mountain, lake, or river, you can't build the Aqueduct. However, you can build multiple Neighborhood Districts and they will count towards the 12 you need. For ease, however, you may want to settle your "District 12" city in a spot with a lot of land space and resources, few mountains (maybe one for an Aqueduct), and access to a lake or ocean (for the Harbor).
For reference, here's a list of the districts:
City Center *Built automatically when you activate a settler, does not count towards achievement*
1. Aerodrome
2. Aqueduct *Not required*
3. Campus
4. Commercial Hub
5. Encampment
6. Entertainment Complex
7. Harbor *Requires settlement near a lake or ocean*
8. Holy Site
9. Industrial Zone
10. Neighborhood *Can build multiple*
11. Spaceport
12. Theater Square
The Colosseum must also be built in the city. It is available in the Medieval Era and must be built next to an Entertainment Complex with an arena building. If you built it or captured it and aren't sure which city it belongs to, just hover over it and the contextual menu will tell you. You may want to play on a map with abundant resources to make it a bit faster to build everything. Also, note even after you win a game you can keep playing and build out your cities and still get the achievement. It can take a long time to build each district, but hitting the "Just one more turn..." button takes away the stress of having to try to complete the achievement before a victory is accomplished.