I'll note down each challenge, what it's about, and how I beat it. If there's anything wrong, please let me know.

Just so you know, beating other challenges, unlocking more characters and their items will make those items available for the Afterbirth challenges, making things easier.

Note: If and when I say: "reroll the floor/run" this means to hold down the R key to restart your run.

Stipulation: Every floor has a significantly increased amount of rooms.
Treasure Room? Yes.
Goal: Beat Mom's Heart/It Lives!
Reward: Gold Heart
Tactic: Curse of the Labrynth (XL floors) won't make floors anymore of a pain than they already are. Use this to your advantage. Be proactive and seek out treasure and curse rooms and work your damage up in order to make the run go along smoothly, but don't forget the Emperor Tarot Card exists. This and a Blank Card can make you finish this run very fast if you already have the damage/fire rate/item necessary. Shops will be your friends because of the sheer amount of rooms available in each floor. Lucky Rock and/or Petrified Poop can make farming the necessary pennies super easy.

Stipulation: Negative effect of Broken Watch is always active, enemies and their projectiles move twice as fast. There is a 16 minute timer that ticks down and once it reaches 0, you'll begin taking a tick of damage every few seconds.
Treasure Room? Yes
Goal: Beat Mom's Heart/It Lives!
Reward: Get Out Of Jail Free Card
Tactic: Reroll the floor until you get Ipecac. Pick your battles accordingly, bomb your way through doors to avoid wasting time. Use your time to seek out treasure and curse rooms, but no more than that. If you keep tabs on the timers and carefully manage your Ipecac shots, you'll finish the challenge with 4-6 minutes left on the clock.

Stipulation: Blindfolded. Play as ???. Start with Pyromaniac, Mr. Mega and Kamikaze!
Treasure Room? No
Goal: Beat Satan
Reward: Gold Bomb
Tactic: I'm going to assume you know how to properly play as ???. The run will consist of mainly mashing space bar in order to clear rooms, but just like with Speed!, remember to pick your battles. Some enemies will not take a lot if any damage from the Kamikaze! blast, so forget about fighting every battle (at some point you'll find rooms you can't clear because you can't reach enemies anyway). Satan's second and third form for one reason or another will not take damage from Kamikaze! so be sure to ration/bolster your bomb supply. Mr. Mega is going to win you the run, so visiting shops for Bogo Bombs or Humbleing Bundle will save you some pains.

Stipulation: Start with Money = Power, Sack of Pennies and the Pay to Play item (every door save a few exceptions must be opened with 1 penny). Start with 50 pennies.
Treasure Room? No
Goal: Beat Isaac
Reward: 2 new pills
Tactic: Don't be afraid of entering shops. There are things such as Piggy Bank, Humbleing Bundle, Fanny Pack and other buyables that will improve your money farming abilities. Don't forget your damage largely depends on your money count, but it won't be the only source as the run progresses. The Counterfeit Penny trinket and/or the Swallowed Penny can help a lot here.

Stipulation: Red health maxed (12 red heart containers), but only 1 container is filled. Start with Charm of the Vampire. All red heart drops replaced by double pennies. Can only heal by Charm of the Vampire.
Treasure Room? Yes (Thanks for the correction!)
Goal: Beat Mom's Heart/It Lives!
Reward: 2 new pills
Tactic: You start with a very precarious situation: You won't be able to heal conventionally unless it's by killing many enemies per half-heart you want restored. You'll want to hang around big rooms with tons of enemies but mind the risks. Go for Devil Deals/Guppy's Paw as soon as possible, because taking away your own red hearts allows you to pick up Soul/Evil hearts, thus increasing survivability. Dark Bum is pretty much useless since there are no red heart drops though.

Stipulation: Start with Key Piece 1, Key Piece 2, Trinity Shield, Mom's Knife, A Ladder and The Boomerang.
Treasure Room? No
Goal: Beat Mega Satan
Reward: Poker Chip
Tactic: Plan to head on to The Chest; I find it very convenient for bolstering your end-game run. If you find Undefined you are able to Error Room yourself out of the Cathedral and into The Chest without wasting time fighting Isaac. Remember your shield makes you impervious to bullets from the front, but it'll switch sides as you correct your aiming. Face enemies head on. Replace your Boomerang after the first few levels, since the ladder will let you access pretty much most islands for items. Mega Satan should be a breeze if you've been picking up just a handful damage upgrades. You'll want the Wafer and/or high HP to secure your victory if you're not confident about dodging the bosses during the Mega Satan fight though.

Stipulation: Blindfolded. Play as ???. Start with 3 Bob's Brain and Thunder Thighs.
Treasure Room? No
Goal: Beat ???
Reward: Stud Finder
Tactic: You're going to The Chest, so don't forget to pick up the Polaroid after the Mom Fight. This run is very difficult because A) Bob's Brains have a long respawn, B) Bob's Brains have a delay after room spawning/respawning before they can be fired, C) Bob's Brains' blasts can hurt you unless you have Pyromaniac and D) Bob's Brains are a stupid way to attack. Ignore my salt and walk over any pots, skulls and tinted rocks you may find in order to find extra resources and precious Soul Hearts to replenish your health. Finding the Relic, the Wafer and any other item to bolster your survivability is important but not terribly necessary. Just having one of those will be enough. Always keep a distance, weave around your enemies and time your strikes because otherwise you'll die to your own weapons.

Stipulation: Start with 3 Dollar Bill, Rainbow Baby and Rainbow Worm. Trinket can't be replaced/dropped.
Treasure Room? No
Goal: Beat Mom's Heart/It Lives!
Reward: D8
Tactic: Your tears are heavily randomized, but they hardly will impact you negatively. This is mostly a Purist run with a few advantages, but nothing you will really have problems with. Finding Brimstone/Epic Fetus can pretty much trivialize the whole thing.

Stipulation: Play as Judas. Start with Chocolate Milk. Tears that hit indestructible obstacles/walls/floors will damage you by 1 tick.
Treasure Room? Yes
Goal: Beat Isaac
Reward: Kidney Stone
Tactic: You start with only 1 red heart, so be careful from the get go. Having your tears always charged can be useful, but risky. If you let go of a tear that will hit "air", then you can quickly quit and resume, and you will not have taken damage. Don't grab any item that gives you piercing effects, neither Polyphemus, because tears that go through enemies will likely hit "air" and damage you. Bolster your HP asap and avoid picking up any source of support damage that might screw your timing. Familiars might kill an enemy you just shot at, so they'll be a source of stupid self-damage most of the time. Ignore anything that helps you kill things unless it's raw damage for your tears. While Ipecac/Mutant Spider/Inner Eye/Loki's Horns/Mom's Eye are usually welcome, skip them this time around. Save your Book of Belial for boss fights.

Stipulation: Blindfolded. Start with Spear of Destiny, Holy Grail and Punching Bag. Start with Isaac's Heart attached to Punching Bag.
Treasure Room? No
Goal: Beat Mom's Heart/It Lives!
Reward: Blank Rune
Tactic: This is a high risk, very difficult, luck-based run because Punching Bag (PB) loves running headlong into enemies, explosions, spikes, fire, literally anything that can kill him (and by extension, you). You'll want to stay on top of PB most of the time, blocking incoming shots and providing cover, but don't be afraid to go all out against rooms with easy/slow enemies. Rooms with traps are basically a timer with PB trying to kill you, so dash for contraptions/exits as fast as possible. Your damage sucks, but there's a trick to near-double your damage potential. Spear of Destiny works like an unfirable Mom's Knife, and as such it has the same capability to be "flailed" around. Hold down a firing direction and then begin repeatedly pressing any other direction to make Isaac quickly "slash" in an arc. The arc becomes wider but slower if you press the opposite direction (e.g.: holding "Fire Left" and mashing "Fire Right"), so go for smaller arcs to slash your foes to pieces. This is useful to clear rooms full of enemies, but the technique shines against stationary bosses such as It Lives!. Be sure to increase your red heart containers, but don't forget soul/evil hearts are a cheap way to survive. Grabbing Gimpy and The Jar will increase your survivability by providing a way to carry health and produce health on kills, while also replenishing soul hearts when hit. Be patient with this challenge, it's doable. Reroll the floor for a Basement if you're having trouble getting the starting tailwind.

Hope this helps everybody. Good luck and don't give up!