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.
Examine the specimens in the second-floor basement
See the "If" Ending
Unlock a secret event...
See the True Ending
Unlock image: "Charm Of Happiness"
See Bad Ending 1
See Bad Ending 2
Get chased by father
Read mother's love letter in the second week
Give the dog a bone
Give the pendant to mother's corpse
Receive a present from the mysterious plant
Help the hungry boy
Rescue the corpse from prison
Rescue the large man
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"