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.
Taken the first photo
Developed the first photo
Observed an in-house object
Dressed in Martha's clothes
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
All diary pages read
Completed all telephone calls for obtaining information
Discovered the house in the woods
Every newspaper edition read
Played the first puppet theatre sequence
Entered the family crypt
Played the second puppet theatre sequence
Communicated with the White Lady
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
Completed the games story