Increases HP by 1 and gives 2 soul hearts.
Trivia: This is a reference to "Bandage Girl" from Super Meat Boy, another game Edmund McMillian worked on.
Rarely Found in Boss Rooms.
Unlocked by killing four Horsemen in one playthrough, not just by collecting four Meat Cubes.
This can be pretty tricky given the random nature of the bosses. The four bosses you need to kill, like the quote says, are four Horsemen; War, Death, Famine, Pestilence or The Headless Horseman. Any combination of these will suffice. (credit to Mr Smooth for the Headless Horseman and combinations)
Sadly, encountering all four of them in a single playthrough is entirely random without the aid of The Book of Revelations, as mentioned by Timothy Roy.
According to comments on the wiki, "Everything is Terrible" makes alternate colored monsters and bosses more common. This is actually good, because alternate colored monsters tend to leave drops on kill.
According to the mechanics guide, it also makes Curses more common in Wrath of the Lamb.
Additionally, however, bosses drop one less heart pickup (heart, half-heart, spirit heart) than they previously did.
My original answer stated that this would not work, but I have discovered that is incorrect. Poo piles that Larry Jr drops will in fact drop items. So far I have only observed hearts and soul hearts, but I would assume that the drop rate is the same as that of any other poo piles. The piles will drop items if the player pops them or if Larry pops them.
It may be slightly impractical to farm items this way because if you shoot at the poo piles you risk hitting Larry and possibly killing him, and you have to get hit infrequently enough to make up lost health with item drops.
So, it seems that you are correct that you could eventually fill the heart meter with soul hearts, but it would probably take a very, very long time.
Best Answer
From The Binding of Isaac Wikia:
This can be pretty tricky given the random nature of the bosses. The four bosses you need to kill, like the quote says, are four Horsemen; War, Death, Famine, Pestilence or The Headless Horseman. Any combination of these will suffice. (credit to Mr Smooth for the Headless Horseman and combinations)
Sadly, encountering all four of them in a single playthrough is entirely random without the aid of The Book of Revelations, as mentioned by Timothy Roy.