Here is the full list of all 22 Martha Is Dead achievements. It takes around 6-8 hours to unlock all of the achievements on Windows.
Completed the games story
Played the second puppet theatre sequence
Played the first puppet theatre sequence
Entered the family crypt
All diary pages read
Every newspaper edition read
Communicated with the White Lady
Developed the first photo
Taken the first photo
Dressed in Martha's clothes
Observed an in-house object
Taken all IR photos with hidden riddles
Taken all 4 IR photos of the lady
Taken a photo with every camera accessory
Completed Lapo's quest
Completed all telephone calls for obtaining information
Discovered the house in the woods
Collected all camera accessories
Fixed the bike
Carried out a divination every day
Taken 5 photos with no story link
Developed 10 photos with no story link