This was a tough achievement for me. I must have tried a dozen times. None of the strategies on the nets worked for me, but I finally cobbled something together that did the job sweetly. I used the Mongols and the It's Money that Matters scenario to win a Domination Victory by 400AD on King level. In a nutshell,  the Mongols give you a large number of cities, and the scenario gives you the cash to build roads and rush build units. I like to explore maps, so this strategy was a good fit for me. I also didn't do any of that save, explore, remember where the capitals are and reload crap that some resorted to.

Research for horsemen. Rush build warriors and capture as many barbarian camps as you can: with the Mongols, these turn into actual cities for your empire. Use that wad of cash to build roads between them and explore. This is a simple way to generate a large number of units quickly and move them to where you need them to be. Mobility is your friend. Following that sentiment, you should build horsemen armies as soon as you can. When you find your first opponent, run in there with a pair of armies (or more, if it took you a while to find your opponent). When you win, you get their unspent wad of cash. This means you can rush build with wild abandon, spending crazy money like my girlfriend when she's at the mall or on amazon.com. Expand your frontlines.

When you have a moment to breathe, rush build a couple Galleys to explore the coast lines. Generally there's at least one opponent on a different island so it's good to start hunting for them. Galleys will also convey a few interesting bonuses if you hit upon ancients. Research Mathematics for Catapults and Writing for Spies to destroy fortifications before beginning a large assault. I found the Greeks and Aztecs to be particularly bothersome. Once you get this far, your research is pretty much done. You can get Bronzeworking and build Barracks in a few locations -- only one of the three units making up an army needs to be veteran for the whole army to be veteran. You may find it valuable to go for Navigation next, as a Galleon is required to search open seas, they're faster, and they can lend naval support to land attacks. Keep building large numbers of units, because your final opponent will often be the toughest, having been left alone reinforce his capital.

Never sacrifice a unit on a barbarian camp. If your down to one man and his attack is blocked, just retreat and heal. Barbarians don't get upgrades when you retreat. However, your opponents do, so you should almost never retreat then unless you're about to lose a premium unit who just got unlucky. Before you have Catapults and Spies, you may cross across a heavily defended city. Sometimes you can take them out by sacrificing a few units; you'll lose some units, but you'll often cause enough damage to make subsequent attacks more effective. (Don't try this against the Aztecs, who full heal on a victory). Always try to win a city on one turn, otherwise the city defenders will heal. Identify your opponent's borders and avoid making first contact with them. Surprise is your other friend. That means hit the hilltops, and stay a few squares away until you're ready to attack. I suspect opponents are more likely to rush build if they can see you lingering around with a few armies. You could try smoking a cigarette and looking casual, but I think you're better off amassing your units just out of eyeshot and then moving all units forward as a whole. 

Remember, you only have to capture one city per opponent to win the game: the capitals. Focus your best effort on the capital city. It's sometimes helpful to capture a smaller city first. You can then use that city as a forward base, building roads to it in preparation for a larger assault. Your troops will arrive sooner, and they'll be in a better mood too. Nothing worse than cranky horsemen. I advise you to not bother building archers or fortifying your cities with defenders, unless you have to. It's better to assault the cities that threaten to counterattack and keep your troops advancing forward. With horsemen and roads, you'll find it easy to chase down an enemy who slips behind your lines.

Using this strategy I also pulled out a "Absolute Power is Kind of Neat" achievement, for sticking with Despotism the whole time.