This is a story related achievement which will unlock with natural story progression.
After talking to Bulling in the Wasps Nest you will exit to a cut-scene. Find out the information you need and make your to the boarding house. Once you enter Tumblety's room, you will see a large travel case to your left. You will need to enter the following dates and information to unlock the case:
12.04.61 - Red Flag, Blue Cross - Grey Hat
17.09.62 - Blue Flag, Gold Eagle - Blue Hat
02.05.63 - Blue Flag, Silver Star - Brown Cowboy Hat
03.07.63 - Green Flag, Gold Harp - Green Hat
04.07.63 - Blue Flag, Eagle Crest - Blue Cowboy Hat