In Dobuita, there is a games arcade.
Hang On is the motorcycle that when you ride you can choose to enter an amount of money. (+ to add credits, - to subtract credits, up to put to max)
Press X when you're ready to play and press Start to play a game of Hang On.
You should get the trophy on the menu screen.
But if you want to play, R2 to accelerate and left stick to control and lean.
Have fun!