Invincibility
Make sure your difficulty setting is set to at least "normal" and then complete your ranking to 23/23(you may need to beat the game a few times to do this). After you get your last ranking, you will be able to endure all damage except falling into a pit of nails or falling into a hole. 

Level Select
Successfully complete the game to unlock the "S-Continue" option that allows any level to be played again. 

Play as a Girl
To play as a girl, beat the game and watch the credits roll by. The girl will be available when you start a new game. 

Play as a boss
To play as a boss beat the game on the hardest difficulty and let the credits roll by. When you start your next game the boss will be avalible