There used to be a solution posted for this method, but for some reason it was deleted. I figured I’d post it up myself as I think it’s the easiest way to get this achievement.
First you will need to delete your cache, which will remove the updates. Yes, you’ll have to update all your games again when you play them next, but that’s the price you pay for an easy achievement. Press the xbox guide button, go to the settings tab on the far right, and then to system settings. Then go down to memory and then go down to the memory device you use (presumably your hard drive), but don't select it. Instead, press Y for device options and select clear system cache.
Deleting the update will make it so that whenever you join a settler unit into an existing city, it will add exactly one unit of population. This will be a larger increase than usual, which is only a portion of a population unit.
So here’s how to do it: choose the It’s the Money That Matters scenario, king difficulty, Roman civilization. Having the Romans is a must because they start with the Republic government which allows settler units to be built per one unit of population. Other governments will require 2 units of population per settler units.
You will need to start in a large, open (preferably grassy) location. The key will be to surround your main city with 3 smaller cities. The purpose of the smaller cities will be to build settler units whenever their population increases to 2. You’ll need roads going from your main city to each of your smaller cities, and send the settlers from the smaller cities to the main central city, and add them with Y. With each one, the population of the main city will increase by 1. By the birth of Christ (year 0), your city should be level 25 or higher. At this point, you will need to optimize your city for gold, which you will be producing via the market, bank, and trade fair you will have been building in the meantime. At this point you will be probably be producing over 1000 gold per turn. You’ll spend about 15 turns making money (at this point, there will be 50 years passing per turn) until you get 20k, at which time you’ll build the world bank and the achievement will be yours.
I’ve done this for myself and 2 friends and each time I’ve gotten the victory at around 600AD. When your city becomes uber, you’ll get a nice torrent of great people which will help you out in various ways. If you’re lucky you can double your gold production and you could conceivably build the world bank before the birth of Christ (imagine that). If other civilizations are attacking you, which never happened to me, it may be smart to just restart. The match shouldn't take much more than 30 minutes.
Good luck and happy achievement hunting! Any questions, leave a comment and I’ll try to answer. If you leave a negative vote please comment on how I can make the solution better. Thanks!
Edit: If you want to have the time stamp for the achievement, save the game right before you win, then install the update again, load it up and get the achievement. Credit to British GM for confirming this.