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