The Item Book is similar to the Monster Book in the sense it records data of all the items you've held in the game. This ranges from gear to materials and consumables. Even key items are kept track of in this record. Thankfully, you only need to get 700 entries rather than filling out the whole book. It's a majority of the entries however it's not quite 100%.
Key items will be easy enough, given the fact you're handed them along the way. Though you may want to note there are a few that come with particular sub events, it's for this reason you should do as many as possible even after your trophy unlocks.
Materials are fairly easy if you make sure to collect loot in each and every area along with defeating your fair share of monsters to get each areas respective materials. You can't buy these with the exception of trading jet black feathers for the higher tier items, so keep an eye out!
You'll have to upgrade each of your shops to 100 in order to have access to all of the gear. Personally, I'd suggest leveling them to 100 and then start purchasing the ones you haven't already had because by then you'll have a discount on all of the gear except the top tier stuff. Each of the shops count and make up a hefty chunk of the list, so get to grinding! Personally, I found the Magus Zero area to be the best for farming materials to upgrade the shops. The item shop won't have much you missed out on if you kept an eye out for chests and what not along the way, but it can't hurt to look!
Lastly are your Fashion items, which are earned from sub-events,Aifreads treasures and completing both story modes in the game. Pre-order incentives and downloaded content are not included in the item book.
This can be done across two playthroughs, so don't sweat it if you didn't max out the shop your first play or pick up enough gear. It helps to save your shop levels using grade for the next playthrough so that's less you have to grind later. Chances are this will be one of your last trophies, but it's nothing you can miss as each item is added to the book as soon as you've touched it. Given the leeway I'd say you can miss some of the sub-event stuff, but I'd suggest going for them regardless as it has it's own respective trophy.