Case 3 Achievement:
As soon as you get in town on case 3, head into the saloon and speak with Bonnie the bear behind the counter. Talk with her about the pictures on the wall and then after the conversation click on each of the pictures on the wall next to you, once this is done a new picture will appear which is the haunted picture. Click on the new haunted picture and then give it to pistol in the same room and this achievement will pop.
Be aware if you do any other activities in town prior to this then you can block this achievement, so don't give pistol anything except the haunted picture first.
If you need help with this then my video guide below begins at this: