What counts as the Dawn of the Planet of the Apes?
Unfortunately on windows it is currently bugged on PC but it is fixed for iOS. (unfortunately it may seem its fixed because people have it but it is a very low proportion which suggests they cheated it in.)
The achievement is quite simple to get if it is the same as iOS
You simply have to have a world where Apes dominate, basically more apes than people.
Try and make sure that you have a lot of apes just to be sure