Some more information I found on the reaper.
"It IS possible to kill Death (a.k.a., the Red Reaper), you'll unlock a hidden character when you do (Easiest way to figure out when to let the run end, is notate the kill count as soon as the monsters despawn). However, doing so is a MAJOR challenge, and here's why:
It's max HP is 655,350, MULTIPLIED by your character's level when it spawns.
It does 65,535 base damage. No amount of armor will save you from that. The only way to get around that is just not taking damage in the first place.
It has 1200 movement speed. You can't run from it.
High levels of knockback are actually bad against it, because it has negative resistance, meaning it will instead be pulled towards the player when hit.
It CAN be frozen, meaning the Clock Lancet (Weapon) and Orologion (Clock pickup from breakables) are essential to being able to kill it.
Another reaper will spawn every minute after the kill screen starts (31:00, 32:00, etc.). These will have different stats to the first reaper if the player leveled up after the first one spawned.
There are a few methods you can use, but the general rule is that you need to stay as low-level as possible until after it spawns, and as Panther said, Laurel and Clock Lancet are really good to get (If you don't have most of your re-rolls unlocked, it might be good to get those before trying this challenge, just so you can try and get what you need somewhat more reliably.
Also, don't try this with Curse leveled even a little bit. Save yourself from that pain, don't make the same mistake I did." - Taylor Swift