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