At the end of each case a letter is sent to you and awaiting you to look at it at Baker Street over the fireplace. You do not have to read any of them. The achievement is for receiving the messages rather than reading them. You will get this immediately upon completion of Case 3: Blood Bath, during the load screen for the start of Case 4: Abbey Grange Affair.
Achievement - Blood and Ice - will unlock just before this one. You should not be able to miss this as long as you finish Case 3.