Early on in the story, after you get saved by Nanba, Nanba will begun to teach you how to make money and introduce you to a Can collecting mini game.
You will be introduced to a character named Kan-san who loves under a bridge close to your current housing, he runs the mini game.
Simply play the mini game in each of the difficulties Easy, Medium and Hard. It does not matter what score you get to earn the trophy all you must do is complete each difficulty.
Upon completion if you choose to max out the minigame ranking you can use the credits you earn for competing each course to buy items and gear from Kan-sans Black Market essentially.