Here is the full list of all 21 Mad Father achievements. It takes around 5-6 hours to unlock all of the achievements on Windows.
See the "If" Ending
Unlock a secret event...
Read mother's love letter in the second week
Give the dog a bone
Rescue the corpse from prison
See Bad Ending 2
Give the pendant to mother's corpse
See the True Ending
Unlock image: "Charm Of Happiness"
Get chased by father
See Bad Ending 1
Receive a present from the mysterious plant
Help the hungry boy
Rescue the large man
Examine the specimens in the second-floor basement
Read the New Text on Anatomy
Help the eyeless girl
Read Maria's diary
Talk to the muttering old man
Unlock image: "It's Behind You"
Unlock image: "Mother's Portrait"