Unlike in previous Persona games, there is an extremely easy way to "kill" the Reaper in Persona 5. The main reason is due to the occasional weather conditions that affect the shadows in Mementos. One of these conditions is Flu Season, which gives all encountered shadows a chance to enter the battle Despaired.
Despair is particularly useful because it causes the affected person/shadow to:
- not attack during their turn
- lose a portion of their SP each turn
- die on the third turn of being Despaired, if it's not cured in time
Thus, the easiest way to defeat the Reaper is to let it succumb to Despair.
From users in this thread, the days that are considered Flu Season are:
On these days, you can simply wait for the Reaper to spawn and attack it. However, it's not guaranteed that it will start the battle Despaired. In order to prevent getting killed, it's very helpful to rank up the Star Confidant to max rank, as it will give you the ability to escape all battles (excluding bosses) with a 100% success rate on the first try.
With this ability, you can simply keep running from Reaper battles until it starts the fight Despaired. Once that happens, you can simply have your entire party Guard for three turns until the Reaper succumbs to Despair.