This achievement is MISSABLE. To unlock it, you need to have five items in your inventory at the same time (as stated in the description). You can only do this in the second chapter chapter of the game (Santa Maria Delle Grazie), in the second half of the chapter. I did it by gathering the handle, metal ornamental dome, lion head, special key and the winged key (as shown in the video).
Hoarder Achievement:Full walkthrough of the game: