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