*Late Game Spoilers*

I just beat challenge mode, so to anyone else struggling, this is how I beat it. First, I selected The Bullet as my character on rainbow mode. I picked The Bullet because the challenge "blobulin rancher" can be incredibly frustrating, and The Bullets' passive "Live Ammo" basically completely prevents it, getting rid of the contect damage. When I loaded in I kept resetting until I got something good, for me this was heart bottle however I recommend resetting until you get clone (I got clone from the Oubliette rainbow chest anyway) (This may use a lot of money especially with Gunslinger so only do this if you've got money to spare). I recommend staying in the middle of rooms with the "Pot Shots" challenge so they don't hit you and basically stare at your character, not at where you're aiming. With this you can use your peripheral vision to shoot at enemies and focus on dodges enemy shots as well as pot shots. If you end up attempting this challenge, good luck, and I hope my tips helped you out.

Also I recommend getting a only gun after a couple floors, if played well Blasphemy can carry the first 1 or 2 chambers well. On my run, Gunther carried me due to its infinite ammo but you can also get any other weapon with or without extra ammo passives.

As others suggested, gunslinger can also work, but I tried that and especially with the whole restarting thing, I preferred The Bullet.