As you encounter new enemies in the world, you can use an item called "Magic Lens" or an ability such as Raine's Inspect Magic in order to gain information on encountered enemies, which in turn adds the information to the monster book.
While completing a play through on the Plays Station 3 version of the game, I used the following link to complete the monster list:
http://aselia.wikia.com/wiki/ToS_-_Monster_ListNOTE: This achievement is missable as some monsters on the list are plot related, such as bosses. It is important to make sure that you always have a few magic lenses or make sure that Raine is in your party and has learned the Inspect magic ability