For this trophy, you need to see all of the game's illustrations except for the ones labeled "EXTRA" (I'll explain what that means later on). They're found in loading screens and a random one displays at every screen so you're pretty much just relying on chance here.
If you're going for the Platinum trophy, then I wouldn't worry about trying to get this one unless it's the last one you need. But if that's the case, then here are a few tips to help speed up the process:
> Enter and exit the shop. - You get a loading screen for going into the shop and then another for going back to the main menu.
> Install the game data to the HDD. - There's an option to do so in the Other Menu and it'll take up about 3GB. Honestly, I hadn't noticed much of a difference in loading times doing this. But if you have the storage space, eh, might as well; you can just delete it afterwards. If not, then don't worry about it.
> Turn off Autosaving. - Before going back to the main menu, the game usually takes a few seconds to save before it takes you to a loading screen. Be careful with this one, though. You could potentially unlock a new illustration without realizing it and end up turning off the console without saving.
You can use the Art Gallery book (which you unlock by beating "Cat Food" in the Rhythm Game) to keep track of which illustrations you've gotten. Then once you buy it from the shop, it's located in Diva Room > Menu > Gadgets. Remember that if one is labeled as "EXTRA" (which are all located at the bottom of the list), then it's not required. "EXTRA" just means that they're exclusive to the PS3 version of the game. Anyways, for me, the trophy unlocked when I went back to the Main Menu.