Here is the full list of all 28 Ancient Cities achievements.
Reach a population of 25 inhabitants
Reach a population of 50 inhabitants
Reach a population of 100 inhabitants
Survive 1 year of gameplay
Survive 5 years of gameplay
Survive 10 years of gameplay
Survive 20 years of gameplay
Survive 50 years of gameplay
Build 5 houses
Build 10 houses
Build 25 houses
Build 50 houses
Build 100 houses
Build all the building types in the game
Achieve 5000 points of fame
Achieve 25000 points of fame
Achieve 100000 points of fame
Achieve 200000 points of fame
Achieve 500000 points of fame
Starting at Mesolithic
Starting at Neolithic
Starting at Ice Age
Starting at winter
Starting at spring
Starting at summer
Starting at autumn
Your tribe has reached the Neolithic
Your tribe has ended up under the sea