Here is the full list of all 48 Murdered: Soul Suspect achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Completed the first investigation
Used Mind Read for the first time
Became a ghost and met a strange ghost girl
Collected an artifact
Collected 10 artifacts
Collected 25 artifacts
Collected 50 artifacts
Collected 75 artifacts
Collected 100 artifacts
Collected 150 artifacts
Collected all of the artifacts
Revisited the scene of your murder and discovered there was a witness
Found the witness and learned what she knew
Helped the witness escape the police station and gained an ally
Discovered what happened to Sophia
Learned the fate of Rose and helped Iris escape the asylum
Discovered links between the witch trials and the Bell Killer murders
Investigated the murder of Iris
Discovered the Bell Killer's secrets
Stopped Abigail and saved Rex and Joy
Helped Ingrid find peace
Helped Julie find peace
Helped Brad find peace
Helped Katy find peace
Used Remove for the first time
Used Reveal for the first time
Possessed the cat
Used Poltergeist for the first time
Interrogated a ghost for the first time
Defeated a demon
Teleported for the first time
Learned about Ronan's Life
Learned about Baxter's Life
Learned about Rex's Life
Learned about Cassandra's Life
Learned about Julia's Life
Learned about the Bell Killer
Discovered Salem's history
Discovered information about the witch trials
Discovered the meaning of the supernatural graffiti
Uncovered the Watery Grave ghost story
Uncovered The Bell Tower Banshee ghost story
Uncovered The Heirloom ghost story
Uncovered the Man in the Box ghost story
Uncovered The Terror on the Tracks ghost story
Uncovered the Eternal Flame ghost story
Uncovered The Stalwart Specter ghost story
Uncovered the Ashes to Ashes ghost story