I started to clear some of the challenges.
The first one, Pitch Black was surprisingly hard as you have to
On top of that, you don't have access to shops. You might not think much of it but it means less upgrades availables and much more trouble to make good use of your money.
Challenge usually ban access to item room instead.
In the end, I had to get carried by
to succeed. ^^;;;
Second ones was High Brow which is basically a challenge with
.
Third one is Head Trauma which basically make you a Touhou character.

For extra lolz, I got Cancer somewhere in there. :V
You start with max tears and range but it's seems you can't raise your attack power in this challenge.
I don't know if it's a limitation of the items you start with or if it's something enforced by the challenge itself.
The Fifth Challenge is
which is unlocked
The Sixth Challence is
I wasn't able to beat that challenge yet due to it being quite different from the rest.
Also, this one requires you to beat Mom's Heart. @-@
I think I will come back to this one later. ^^;;;
The Tenth challenge is Cursed! which you need to unlock
as well) to access and for good reason :
Spoiler:
]the whole game is under the effect of Curse of Curse which put spike doors on... well about mostly every door.
To make up for this, you start with full map, Child heart and Yum Heart.
Are you able to make your way to mom in a single piece? : P
Will you choose to skip many treasure room and shops?

Also, while you can find Trinkets and Space Bar items, you might not be willing to trade them away. X D
That being sad, I traded Yum Heart for Guppy Paw which in the end gave me enough life to last that ordeal.
Pro tip : you might want to use some bombs to go through secret room, saving some life in the process.
The twelth challenge is When Life Give You Lemons. Basically, it's a Lemon Mishap (spelling?) challenge.
That item was buffed compared to the original version of the game so it's not that hard of a challenge, especially since you can spam it.
That being said, I met more flying enemies that I would have like to. X D
Some of the items unlocked by the challenges are
which are a "Q" item like Tarot cards.
I got to try 2 of those. One apparently