For this trophy you'll need to start up 'Challenge Missions' which is located under Free Battle mode.
Now among these missions you'll unlock an image piece for each one you do, and upon accumulating 10 you'll form a complete image that you can install and use as a Theme on your dashboard! Which is so freakin AWESOMESAUCE!
The first 10 missions have various conditions to completing but are the easiest, and pretty straight forward. You can also choose from any of the characters you have unlocked, and use items/bentos to boot.