The bestiary is a new addition to The Binding of Isaac: Afterbirth † that is accessible through the "Stats" menu. The Bestiary shows information and statistics on all encountered monsters and bosses except for some alternate forms of some enemies.
It shows the number of times an enemy has been encountered, how much health it has, how much damage it has done to Isaac, how many times it's been killed, and how many times it has killed Isaac.
Because Repentance added a lot of new enemies, the whole page layout was reworked, requiring this page to be separate from the Afterbirth † Bestiary.
The order of the monsters starts with Rebirth enemies, then Afterbirth enemies, then Afterbirth †, and finally Repentance enemies.
Encountering a boss while fighting Delirium does not count towards the bestiary.
Seeded and challenge runs will affect bestiary entries, including whether an enemy has been found at least once or not, meaning that regardless of whether achievements are disabled or not, bestiary entries will still be updated.
This also means that enemies spawned using the developer console will be counted as well.
While fighting Hush, the Blue Boil will count as an encounter but the Blue Gaper will not. A Blue Gaper must be found on its own to be marked as an encounter.
These are the monsters on each of the bestiary's pages.
(Click on the images to open the corresponding monster page.)