I've been running through the challenges to unlock things. It's interesting to ask whether this is actually a good idea. Presumably the goal of the game is to do everything, so eventually you will want to do them all if you are going for utter victory, but many of them unlock cards that dilute the card pool. The worst offender is challenge eleven while unlocks the Rules Card which I'm pretty sure does nothing. Once you've done challenge eleven, every card you find has a chance to be a blank.
But anyway, the "challenges" themselves are mostly not so much challenges as easier versions of the game. Many of them only go to Mom, so once you're used to getting to ??? and the Lamb, even with a mild handicap a run to Mom is probably thought of as a given rather than a challenge.
And those handicaps generally are pretty mild. Some of them are probably even advantageous. Basically challenges start you with a small number of interestingly synergistic items, but don't give treasure rooms on the floors. For example, in challenge 16, "Computer Savvy" you begin with Technology, Technology 2 and Spoon Bender which collectively have you piercing homing lasers. This is a complete cakewalk to Mom. Challenge 15, "The Slow Roll" starts you with Polyphemus and Cupid's Arrow giving you massive piercing shots that do huge damage. You also start with My Reflection which makes your shots boomerang, limiting your range, but that's not a big problem.
So far I've completed most of the challenges. That's not much to brag about since the ones I haven't done the ones that seems actually awfully hard:
Six - Solar System - In this challenge you can't shoot tears and you begin with four flies orbiting you: two close ones that block shots, one far one that damages enemies on contact and one mid-range one that does more damage than the farther one. You also start with flight. Basically you have to kill everything with those attack flies, and instead of just Mom, you have to make it to Mom's Heart. This, frankly, seems awfully rough, and this seems like a very genuinely hard challenge. Probably my best bet to win it is to get some alternate form of attack, like a brimstone or even an infested baby. My skill at circling around an enemy, staying close and not getting hit just isn't what it would need to be.
Eight - Cat Got Your Tongue - In this challenge you can't shoot tears and you start with Guppy's hairball which is a thing you can kind of swing around with the movement keys to whack enemies. I find this really, really hard to do. Maybe I can get the hang of it eventually, but it feels like I'm playing a different game. Again, I'll probably win this by getting a baby.
I also haven't completed:
Seven - Suicide King - In this challenge you start with Ipecac which changes your shots in a lobbed poison bomb, Mr. Mega which increases your bomb radius and damage, and My Reflection which makes your shots boomerang. Unlike in The Slow Roll, shots boomeranging is a serious issue since your shots can hit you. In this challenge you have to get all the was to Isaac. I'm sure I can win this challenge by just playing well, but I left it to get to others for now.
Seventeen - Waka Waka - In this challenge you start with Anti-Gravity and Strange Attractor. Anti-Gravity causes your tears to hover in place when fired instead of shooting across the screen. After several seconds, or when you let go of the fire button, the tears will move. Strange Attractor draws enemies and items towards your shots, often making enemies move erratically. So when you shoot your tears stay on top of you, and enemies are pulled in. This is a real mess for dealing with some very common enemies, but I don't think it's overall very hard.
Twenty - The Purist - No starting items, no treasure rooms. You have to kill Mom's Heart. I imagine I can get this in a few tries by just getting good drops. The key to this run for me will be getting damage up items either from lucky boss drops, curse rooms, and devil/angel rooms.
A couple of the challenges I have completed involved a decent run of luck and aren't readily repeatable:
Four - Darkness Falls - This one starts you with a lot of damage items and a fear item, so it seems pretty easy, but you have to get to Satan, and I'm terrible at the Satan fight. Anyway, I basically just crushed this one by getting an insane combination of items that let me get unlimited bombs, keys and heart containers, plus getting a lot of tears up items. I took every devil deal there was and still had seven heart containers at the end of the game, and I was just a killing machine with my excessive damage.
Thirteen - The Bean - This is another no tears challenge. This time you start with Pyro, the Bean, the Black Bean, the 9 Volt Battery, and Butt Bombs. This means you have 99 bombs and your bombs damage and stun everything on the screen. On the other hand, your only way of repeatably attack enemies is by using the poison gas from the Bean, and that only recharges every 15 seconds while in a fight, thanks to the 9 Volt Battery. I thought this would be easy but I kept making it to Mom without enough bombs left to win. Waiting for the bean to recharge to get more damage in against Mom is not easy. In my winning run I got the infested baby, giving me a reasonable repeatable damage source and had 70 bombs going onto the final floor. Then the Bible was in a shop there so it didn't even matter. I think to win this challenge I would usually need either a baby or the Bible. Both was silly.
I've got a run of Seventeen - Waka Waka - half complete with the lump of coal which makes tears do more damage the longer they are on screen and combos very well with anti-gravity. Hopefully that gets me a win and I'll move onto Purist, then Suicide King. After that it'll be back to clearing the boss rush with all characters. I'll leave the two hard challenges for later.