Here is the full list of all 20 Dogs Organized Neatly achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Solve Chapter 8
Solve Chapter 7
Spend at least 2 hours in the game
Solve Chapter 6
Unlock 30 dogs
Spin Garibaldi 4 times in a row
Unlock 28 dogs
Solve Chapter 5
Spin a total of 1000 dogs
Click on a total of 1000 dogs
Solve Chapter 4
Turn on and off the sound in the options menu 10 times in a row
Let any dog bark 10 times in a row
Unlock 20 dogs
Solve Chapter 3
Solve Chapter 2
Unlock 13 dogs
Solve Chapter 1
Unlock 7 dogs
Unlock 3 dogs