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