Here is the full list of all 13 FOX ADVENTURE ~HOMEWARD JOURNEY~ achievements.
Clearing the first level
Clearing the second level
Clearing the third level
Clearing the fourth level
Clearing the fifth level
Clearing the sixth level
Clearing the tenth level
Clearing the twelfth level
Clearing the Challenge Mode
Clearing the Primitive Edition of the tenth level in Special Mode
Clearing the Primitive Edition of the seventh level in Special Mode
Clearing the Special Challenge Mode
Achieving all achievements