Once you discover the location called Ms. Brewster's on the map in Ocean City, head there and go inside. Approach and talk with the woman there until you get the dialogue options to help. She'll give you a room key for the murder scene. Go up and investigate the room, making sure you move the rug to discover the occult circle underneath it, before returning to her. After the subsequent conversation, you'll then be able to knock on each door and question the occupant to try and find who the culprit might be.
No spoilers on the puzzle itself, even though it isn't very difficult. The actual moment that gets you the achievement is afterwards. Once you tell everyone which room the occult salesmen lives in, you'll get a couple dialogue options when he protests his innocence. When he says that he didn't do it, pick the option that does NOT blame him, but says something along the lines of "Of course you didn't" or something like that. When you do, the actual culprit will be revealed and the achievement will pop.
The important part is just that you don't actually accuse the occult seller of doing anything wrong.