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