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