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.
Discovered what happened to Sophia
Teleported for the first time
Helped the witness escape the police station and gained an ally
Collected 100 artifacts
Learned about Rex's Life
Collected 75 artifacts
Learned about Baxter's Life
Helped Brad find peace
Helped Katy find peace
Found the witness and learned what she knew
Uncovered The Bell Tower Banshee ghost story
Collected 50 artifacts
Helped Julie find peace
Used Remove for the first time
Possessed the cat
Collected 25 artifacts
Revisited the scene of your murder and discovered there was a witness
Uncovered the Watery Grave ghost story
Collected 10 artifacts
Helped Ingrid find peace
Defeated a demon
Used Poltergeist for the first time
Interrogated a ghost for the first time
Used Reveal for the first time
Collected an artifact
Completed the first investigation
Used Mind Read for the first time
Became a ghost and met a strange ghost girl
Collected 150 artifacts
Collected all of the artifacts
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
Learned about Ronan'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 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