The new achievements don't work yet, they're just added to the page, not the game.
So, I just completed a 'challenge' run. I was playing as Isaac with no damage ups (I would d6 them away, but I never encountered even one) and no devil upgrades.
I ended up with the worst character I ever had. I kept getting HP Ups, so I had 10 hearts at the end of the run. I did pick up a Battery in a shop, but never found a good spacebar item, so I still had the d6 in the Womb.
One up side is that I got both spider web shots (C.shot, remember, Mega man fans?) and Gish, so all my enemies kept flashing between black and white in an epileptastic fashion.
It Lives took me about 9 minutes of nonstop firing because I just didn't do any damage and I got the worst possible luck with spawns. I think I fought 3 Dukes, 4 Larries and 4 Chubs in total, just during the final boss fight.
So yeah, never doing that again.