The Banshee is an enemy not dissimilar to a genie, although his intentions are to kill you, rather than grant you three wishes. His main form of attack is sending out a stream of homing shots from his hands, and will chase you around the room until defeated.
Before Dahlia was introduced, Banshee was the final boss of the game.
If you land on the Banshees head, it will be almost unable to hit you with any of its attacks. However getting off its head can be difficult