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