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