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