So here's how this achievement works. About 50% of the time when you win a battle, at the end you'll unlock a 'comic book' for one of your characters. These comic books level up one of your character's moves. So for example, if you get a Comic Book of Thor, one of Thor's 3 moves will go up a level. The max level is 5. So you need to effectively collect 15 comic books for a single character (5x3).
Now here's the rub: that 50% chance happens for every character that you have so far unlocked. If you're new to the game, there are over 50 characters. Thus, it would take a long time once you finish the game.
So if you're just starting the game, you might want to grind this out immediately. When you play the first level, just keep replaying it. You can skip the cutscenes by hitting 'X'. Keep selecting the same three characters as they will level up. After you get to about level 10 for each level, it will take you roughly 20 seconds to do this. You should use 3 characters that you want to use more in the game. I achieved this all by about level 35 of my characters (maxed out Thor). The characters you choose to play with do not seem to have an effect on which Comic Book you get. While this may seem daunting to you, I actually found I had to a little grinding at the beginning of the game, so this isn't actually that inefficient.
If you're like me, and you failed to do this at the beginning (and have now unlocked far too many characters), what you'll want to do is start up the game and choose a different save device than what you had previously chosen (e.g., an external hard drive, the cloud). Then just replay the first level until you get it done. This is personally what I ended up doing.
Took me roughly an hour.
After you do this though, you can play normally through the game without any other achievement concerns is the good news.