Here is the full list of all 33 Lumberjack's Dynasty achievements.
Marry a beautiful woman
Cut down 500 trees
Own 25 forests
Own 1,000,000 Euro
Catch 50 fish
Max out all the skills
Exceed 100 km/h in a vehicle
Find 30 treasure chests
Rebuild special community buildings
Plant 50 trees
Learn all possible recipes including unique ones
Expose dirty truths and become a Mayor yourself
Help James with all his resort buildings
Own 10 vehicles
Own the farm and lumber mill
Own a furniture factory
Create 100 wood plank pallets
Help 50 people
Learn recipes from all the cook books
Own over 20 animals total
Own 5 forests
Cut down 50 trees
Help 25 people
Own 5 vehicles
Help 10 people
Repair all of the lumber mill buildings
Own a tractor
Repair all of your farm buildings
Plant 500 trees
Catch 500 fish
Have a kid
Exceed 1,000,000 Social Points
Stand side by side with Mayor and become his deputy