This trophy is to perfect the book hunting mini-game for Kaname. This means you need to fill up her gauge before time runs out and she cannot get hit by any falling books.
This can be a little tough, especially with the controller, since the books are sometime narrow and hard to hit.
There are two strategies to getting this:
First, you can be quick and accurate, shooting books and making sure Kaname doesn't stumble by keeping your cursor over the target box behind her every now and again. This is probably the harder of the two strategies as the PS controller can be imprecise sometimes and it always seems like I run out of time.
The second, and the easier of the two, is to ignore Kaname and just shoot the books. This will cause her to stumble and you will have to make sure to shoot all of the books that fall off of the shelf, but you will fill her gauge much quicker. As long as you don't let her get hit, you should be able to perfect this mini-game with relative ease.
As soon as you complete the level the trophy should pop.
Hopefully this help and have fun!!