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