Here is the full list of all 30 A Matter of Murder achievements.
solve a case where Diva LaVoix commits the crime using the axe
attended your hundredth house party
on a case where there would have been multiple murders, catch the killer before they can strike again
solve a case where Don Amore is murdered for love
solved twenty-five mysteries
solve a case where the murderer acts out of jealousy and uses the poker
solved a crime with audio clues
solved a mystery where the rope was the murder weapon
solve a crime that takes place at the Seaside Villa
solve a murder which takes place in the kitchen
you failed to correctly identify a single element of the crime
solved a generated mystery
solved a Master Detective level mystery
solved a mystery where the pistol was the murder weapon
solved a mystery with multiple victims
solved a mystery where the murderer was motivated by money
you let the killer escape
solved a mystery where Doctor Weiner was the victim
discovered and used a secret passage
solve five mysteries
solved a mystery where Ward Constance was the murderer
solved a crime that takes place in the dining room
solved a mystery where the murder was commited with a blunt object
solve a case when your clock is in the red zone
visited all mansions
you were murdered
searched all rooms of the mansion
solved a mystery where the poison was the murder weapon
solve a case where Master Percy is neither the victim nor the murderer
completed the tutorial