The Adventures of an Irresponsible Hero and a Shadow Girl

Can't go home unless I beat the game by defeating the Demon King? The brutal, savage demon race is about to attack, and humanity is counting on me to save it? I'll get a game over if I don't clear the game before the time limit?

I know all that, and it's pretty important, but what I really want to know is, as a hero, how do I get my own shadow to fall in love?