A lot of people have been asking about this things. They normally make theories and sometimes say the truth, but here I have discovered how to unlock these. It takes determination and skills (for real) 'cause this is HARD.

Unlockable	How to unlock
Afterbirth + bosses and champion variants	Defeat The Lamb
Apollyon	Defeat Mega Satan
Burning Basement	Defeat Mom's Heart 11 times.
Greedier Mode	Donate 500 coins to the Greed Machine