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