This is actually fairly simple and can be earned in around 15 minutes or so. it's worth noting that this doesn't have to be done with different districts; using seven neighborhoods will suffice.
Create a game using the following settings:
Starting Civ: Japan
Start Era: Information
Game Speed: Online
Map: Pangea
Size: Any
No Barbarians
Leave everything else as Standard.
You'll start with a few Settler units along with a few Rangers and Machine Guns. Use one of your Settlers to found a city, and use the other units to scout the immediate area. Use your other Settler units and found cities around 6-7 tiles away from your capital - this will aid in expanding the borders of your capital, making this achievement easier.
Then it's just simply a case of building seven neighborhoods adjacent to each other like in the image below:
Note that you'll need to build the neighborhood in the center last, otherwise the achievement won't unlock.