This Trophy can be very challenging depending on when you go for it and what difficulty you are on. The Reaper is a mini boss-like enemy that can only be encountered when opening your 22nd normal chest which are found throughout dungeons. After you open 21 chests you will start to hear chains jingle. The next normal chest you open might give you a chance at fighting the Reaper. You will receive a warning upon trying to open the 22nd chest if the reaper is inside of it.
If you go up or down a floor after hearing chains or if you don't receive a warning when opening the 22nd chest the counter will be reset and you will need to open another 21 more chests. Opening locked gold chests do count towards the 21 chests you need to open but you can
NOT encounter the reaper from a gold chest.
I didn't fight the reaper until my second playthrough but you can fight him in your first playthrough. I'd recommend being at least level 70+ before attempting this trophy.
(Update) November 17, 2015I didn't think much about this at the time of writing this guide but you can save right at 20 chests so that you can reload your save if you don't encounter the reaper upon opening your 22nd chest.
Here is link to some extra information: http://www.gamefaqs.com/boards/641695-persona-4-golden/69669...