This achievement may not work if you don't have Patch 1.01, as the achievement may glitch and not be acquired (A bug addressed in the patch).
This is easiest to achieve on easy as a Military or Religious creature.
It is also easy to complete if you are an Economic city, and have a lot of spice geysers and vehicles to trade with.
Try to destroy or win over towns on your continent RIGHT when they appear. This won't work with the people NOT on your continent, unless you have a naval fleet and they are a coastal city.
Have highly productive factories by putting many house next to them. Remember, a factory does not make money unless it's directly linked to town hall. Putting houses in the remaining spaces increases production, increases happiness when next to entertainments building, and allow you to have a bigger fleet.
Save up and make air fleet of six airplanes for attacking/winning over each city. Use your special weapon right when you can.
Being a sea city also helps. Take over a lot of sea cities that way.
Use your special ability that takes over all the cities as quickly as you can.