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