He seems to have collapsed on the inside and is bleeding from his eyesockets. Most of them look absolutely horrible, but Peep's design (now known as The Bloat) looks the worst by far.
Isaac has to be blown up by a Mulliboom in the Basement/Cellar You have to perform a sequence of specific deaths with 4 different characters at specific locations: The short version, with just the instructions to unlock the character, is under the spoiler: The Lost is meant to be the most secret and elusive unlockable character in the new Binding of Isaac.