Here is the full list of all 15 Axes and Acres achievements.
Win 50 Matches
Build 20 Castles
Build 30 Houses
Destroy 50 Barbarians
Construct a Theatre
Hunt 30 Rabbits
Construct a Castle
Reach Rank 10
Win 10 Matches
Chop 30 Trees
Construct a Town Hall
Build 30 Roads
Win 3 Matches in a Row
Finish the Tutorial Scenarios
Win 100 Matches