We are Family
Become the dominant Religion in every Capital city on a standard-size or larger map.
I have set up a game on a huge map and my religion was spread over all cities, while 35 of them belonged to me. So my religion was clearly dominant. I also made sure they are dominant in the enemies capital cities.
But the achievement did still not unlock. While the description seems to be very obvious, a lot of people seem to have a problem with it. I found a couple of sites with discussions about it, including civfanatics, but no clear answer on how to actually unlock it.