Conquest of the world
Solution 1:
I've done it on a duel size map, and I assume you have to win a domination victory. My one enemy had only one city, so I can't say it for sure.
There is also no difficulty requirement for this achievements.
Solution 2:
Alright - I have also had this problem for a long time, and I finally got the achievement. It seems as if city states also count as players. As per my comments on the original post, I had won at 1180BC, and made sure that the enemy had no other cities and no other units. Now, without city states, the victory resulted in the achievement.