A beard that is so remarkable and must be photographed, documented, or even commented on, in order to label it with significance; usually for later conversation about how epic the beard was.
Dude! Do you remember that Incredibeard that we saw at the mall the other day?! That guy must have been growing that since 1974!
When something surpasses legendary status; something so awe inspiringly jaw dropping that it will make you shit your pants due to the amount of legendary given off by it's mere presence.
Bob: this sandwich is incredibeast.
Bob: *shits his pants as his jaw drops to the floor in amazenment*