This guide explains how to kill the Reaper and to obtain a Goddess Scythe.
Killing the Reaper
Killing the grim reaper is a lot easier than I thought it was going to be. Here's a guide compiling the information I found on the internet into these simple steps.
Keep in mind you will need to kill a reaper to obtain several achievements, including "The Grim Reaper", as well as "Synthesis Professor" and "Item Hoarder".
The Goddess scythe is not a 100% guaranteed drop and you might need to kill the reaper several times to obtain one.
The Goddess scythe is used in synthesis to create the Holy Omega Sword, which is in turn used to create the Omega Flora Sword, which is the best sword in the game.
The easiest way to do this is with Hinata and her "Legendary Hinata" skill bloom leveled up for her passive "Unbreakable Heart". I'm not sure what the chance is for it to activate, but I was able to use it reliably at skill bloom Level 23.
Next you'll need a couple of specific items;
Luckily, you can easily find these two items on the first floor of Hinata's Trial dungeon, which is pretty convenient.
Doing the Deed
Essentially how this works is getting the reaper to attack and activate Hinata's Unbreakable Heart, while being under the effects of Haste Potion. The potion will allow you to move twice in one turn, so you can swap your HP with the reaper using the wand, then finish him off with Botanical Blaze.
First things first, you're going to want to find an open area near the stairs of the dungeon, I also recommend clearing the floor of every monster so there's fewer stragglers that can potentially mess things up for you.
Here you can see there's a 3x3 open area with easy access to stairs should things go wrong.
Next step is to just wait. Press A+B at the same time to make the turns go by way faster, while killing any newly spawned monsters that enter the room. If you're in Hinata's Trial your belly will be at around 20% when the first "lukewarm winds" arrive, and 9% when they get stronger.
This will take a moment and is a perfect time to pray to the RNG gods.
Here's where you want to start paying attention. I usually take things slowly turn by turn to make sure I don't mess anything up. A few turns later, the music will change to the monster room song and the reaper will spawn.
You're going to want to get him to a spot where he will move on his first action, and attack you on his second action, that way he wont just kill you after Unbreakable Heart. The sweet spot seems to be two tiles away from you. At this point you will want to drink your Haste Potion.
Keep in mind he moves unpredictably and this might take a few tries to line him up correctly.
After surviving at 1 HP, you will be able to take two actions. The first is swapping your HP with the Reaper using your wand.
The second option being Botanical Blaze. Make sure to use Botanical Blaze and not Blooming Heart, as Blooming Heart seems to always miss the reaper.
Now that he is dead, you will have earned the Grim Reaper achievement. If you are lucky, you will have received a Goddess Scythe as well. Make sure to leave the floor as quickly as possible, as more Grim Reapers will spawn after killing the first.
If you are doing Hinata's Trial for the first time, the Scythe will make it extremely easy to complete the Dungeon, just don't get cocky as the Braman Knights in the second half are extremely strong.
After completing the Dungeon, you should have leftover HP swapping wands and haste potions to use in different dungeons. The easiest one to farm them, in my opinion, is Maze-Like Garden, on the first floor by the stairs.