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