You will get the Monster Book once Karol joins your party. Every monster you encounter before and after that point will be put in there, but their pages will not be filled out unless you use a magic lens on them. You can only carry 15 at a time, so be sure to stock up every single time you come across a shop. If a boss goes through various stages, you may have to scan it more than once. Hold down the RB button to see if an enemy has not been scanned, you will know because its HP will not be shown. If you already have it in your book, it will show the HP of the monster. If you encounter a boss-type character more than once throughout the game (the two idiot knights and Zagi for instance) you must scan them every time you encounter them. Be sure to spend 10 in the Grade Shop to carry your book over to any future playthrough.
See this thread for all the monsters you need and where to find them.