All credit goes to thirtysmooth the owner of the walkthrough, but in case you missed it, I've posted it below. This is by far the least button press intensive and quickest way of doing it with every leader.
Instead of selecting ‘Random Map’ from the Game Mode menu, select ‘Play a Scenario’, then ‘Lightning Round’. In this mode you have to be the first to research the ‘Atomic Theory’ technology before anyone else, and it starts the game in the Medieval era. After selecting your civilization and difficulty (Chieftain of course), you’ll enter the game with three cities already built.
I would suggest building three defensive units, and forming an army, in each of the cities so as to protect yourself from any incoming attacks. Once this is done, go into each city’s Control Screen and press on the ‘City Focus’ icon (bottom right of the screen, the icon depicts an apple, gold bullions, blue beaker and a hammer). Once there, press on the blue beaker at the bottom. This will set the city’s focus to produce science. The reason you want to do this is because it will aid in the speed in which you research technologies.
After setting up each city’s focus, you’ll want to add extra firepower to your researching abilities. Building Libraries and Universities add science benefits to each city, so after researching the relevant technologies, focus on building these.
You’ll no doubt attract the interest of neighbouring civilizations who will want all of your cities and, more importantly, your beloved research. They will be relentless in their attacks on your cities, but for the most-part they will only attack you with weak units which your defensive armies will easily be able to withstand. Don’t worry about building offensive military units, unless you feel especially threatened by any of the incoming attacks.
Now, you’re probably wondering which is the quickest research route to take when aiming for ‘Atmoic Theory’. You could make your brain hurt and work it out for yourself using the information in the ‘Hints and Tips’ section of this walkthrough, or you could use the following list (thanks to Musquito for the help with this list):
Code of Laws
* only the Mongols and the Americans require this technology.
** only the French and the Russians require this technology.
Once you have researched Democracy, change your government to this as it will add +50% to science which will increase your speed in researching technologies.
It should now be a case of repelling any attacks made by the other civilizations and racing to be the first to research Atomic Theory. Once you have, depending on which civilization you chose to play as, you’ll earn the below achievements. Using this method takes between 15-30 minutes, depending on how vicious the other civilizations are towards you.