You are able to get this achievement before winning on Deity difficulty. So if you don't mind playing the game a few extra times, play through a game on the easiest mode, Chieftain, and play your heart out. You should be able to get all four wins with out to much difficulty, but still I will give you tips.
- At the beginning of the match, bulk up on warriors and try to quickly take over one civilization. It shouldn't be to hard at the beginning to just lay seige on a city with an army or 2 of warriors and to win.
- Once you've taken over one civilization, build up your defense in your cities and start trying to populate your cities quickly, along with creating a 2 or 3 more cities, (remember you get a free settler once you reach 100 gold)
- Take the time to build a couple of ships to go explore the rest of the world
- Once your civilization is growing and well defended, start bulking up on technology and wonders.
- It shouldn't be too long before you can outclass any civilization on the board. At this point you can save this map as it is, and then focus on trying to obtain a certain win.