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