Unlocked by beating Mega Satan for the first time
To reach Mega Satan, you either need Dad's Key, or the two combined key pieces from the Angel Rooms, explained here
Then get to chapter 6, either the Chest or the Dark Room works. Once you arrive you'll see a giant gold door with a key symbol on it. If you have the Angel Room key, it will automatically float over to the door and open it. Otherwise you'll need to use Dad's Key, which can unlock any door. Head inside for the fight.
It can be a pretty tough fight if you don't have a powerful run going. Mega Satan has a lot of health, shoots bullet hell patterns, occasionally turns invulnerable and spawns in minibosses, including the Seven Deadly Sins and their Super variants, the Harbingers, and dark versions of the Angels. He has two hands that have their own attacks and can be destroyed but respawn after a short time. He also has two phases, in his second phase he doesn't summon minions anymore and loses his hands, but has tougher to avoid bullet patterns.