There are other pages on the internet that list strategies for the different achievements. There are a few good tips to keep in mind, too. What I'll list here is what I would suggest to use against the hardest to complete.
complete by 1000AD on king or higher
win by domination on the hardest difficulty
I've seen other people suggest strategies for winning this, but I think this can be done easier than anything I've read online.
Basically, you only need to take the capitol cities. That's only 4 cities. They're also almost always coastal. If this is played on the Beta Centauri scenario, you don't need to worry about scientific advancement. This is where the computer players really have an edge (time). I like Aztecs because they are never wounded (unless you retreat).
The gist is:
(1) Develop an inexhaustible economy
(2) Scale-up an effectively unlimited manufacturing potential.
(3) Load up a dozen Modern Infantry armies and a few dozen Artillery armies on a fleet of Battleships and head for the first city. At each city, park your Battleship unit and its payload both on adjacent squares and pound the city until it falls. Pick up all but an MI army (to occupy) and move on to the next.
(4) Win the game, gain the achievement.
A few tips:
(1) Part of it is staying away from neighbors. They will tend not to bug you if they don't know you're there.
(2) Encountering one early might not be a dealbreaker. But keep them boxed up if you can, until you're ready to push them aside. On Beta Centauri, the barbarians can even serve to separate them from you. If you do meet stay friendly early.
(3) If you are getting harassed before you're ready to move out, pay others to go to war. Hopefully, it won't come to that. This might happen after you've knocked a couple of guys out already, and its obvious you want to take over the world. You can still pay them off to go to war to stall until you wipe them all out.
(4) Of course, this is all assuming you do keep up the normal defenses. Modern Infantry are great. Also keep Fighters. This includes the captured cities; rush new MI every turn. If you already have the funds, this should be no problem, even if everyone is on you, which might not even happen. Keep up the borders. Of course, everything is armies and wings and fleets, because you should have the production lines to support it.