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