Here is the full list of all 27 Jack Lumber achievements.
Buy all the beards
Get a gold sash for every animal
Buy five pictures for your cabin.
Spend 50000 Logs in the store. (Lifetime)
Get a silver sash for every animal
Get a bronze sash for every animal
Beat World 4
Click the animals in the Cabin 200 times.
Use 50 Syrups
Use 15 Syrups
Beat World 3
Re-watch a cutscene
Learn the names of the people that made this game
Beat a level with three or more beards on.
Read all of the letters from Ranger Bob
Own at least one of every syrup at once.
Read all of the letters from Jill Timber
Beat World 2
Beat a level with one or more beards on.
Spend 5000 Logs in the store. (Lifetime)
Beat World 1
Get a painting for for Jack's cabin
Use 100 Syrups
Hit 10 animals
Get a plaid sash for every animal
Finish all of your errands like a good lumberjack.
Spend 100000 Logs in the store. (Lifetime)