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