Getting an ecstatic city comes from getting amenities for the city. Kind of like happiness from the previous games.
Amenities can come from buildings (Arena/Colosseum), adding the entertainment district, or adding Luxury items to your cities with builders (like incense or silk)
Getting the achievement, you need to have roughly 4 times the amount of amenities required for your city to be happy.
This is determined by population. Right now, my population is 4, and require 1 amenity (it can be found on the City Details screen) so getting 4 amenities then brought me into an ecstatic state, thus unlocking the achievement.