Beating the Beast also counts when you think about it.
Catharsis Factor: Beating Dogma, especially for people who have grown up in fundamentalist families.
By then, however, you'll probably have accumulated soul hearts or even more items from past boss fights, so it's not like the challenge both bosses present really matters. Thanks to the buffs to Kamikaze (its explosive radius was increased and its damage was increased from 40 to 185), the item has gone from an item that can kill practically everything up until the Womb (or sometimes even the Depths), to a clean One-Hit Kill on everything in your path (thus allowing you to lure in even the strongest enemies and let the item rip) on top of curb-stomping most bosses, with only the fights with It Lives! and Satan being legitimately challenging.
The Blue Bomber challenge became this in Repentance.
Fetus bombs whenever you decide, vastly decreasing the chance of you accidentally hitting yourself with your own explosions. The Remote Detonator also allows you to explode your Dr. Fetus, an Infinity +1 Sword that can make short work of almost every enemy in the game and also grants you infinite explosives to search for tinted rocks or Secret Rooms.
The Demo Man challenge is a breeze as you start out with Dr.
The only legitimate obstacle in your way will be objects like rocks, but even then, an item that gives spectral tears eliminates this.
The Computer Savvy challenge is by far the easiest in the game, as you start out with Technology, Technology 2, and Spoon Bender, meaning you fire lasers that curve themselves to hit their targets for you.
There will also always be some empty rooms, and it's possible to spend quite a long time in the arcade with virtually no chance of death.
Breather Level: Even during the Brutal Bonus Levels, there will occasionally be rooms with only a fly or a pair of helpless grubs, which still recharge your special item and have a chance to drop items.