Dramatic Ages is a new game mode that eliminates normal and heroic ages and instead gives you either a dark or a golden age, respectively. What you need to do is get an era score at least 20 points above what you would need to earn your next golden age. So, for example, if normally you need to get 25 era score to get a golden age, instead get 45+ to unlock this achievement. This is easy enough to do starting from the ancient age on settler difficulty. Just keep killing barbarians, visiting tribal villages, building wonders and doing any number of things that will grant you era score.
Here's a large (but likely incomplete) list of things that will grant era score: http://bit.ly/2K9Vkqb