Katamari Forever

There are a total of 4143 items in the game.

When you roll over something you haven't collected yet, the item's name will appear in rainbow colours at the bottom left. Those items are then added to the collection if you successfully complete the level objective.

The vast majority of items will be found naturally while unlocking and playing through every mode in the game. You must do this anyway as every mode will add a new planet to collect in the Wake Up The King! level. I had 98% of the collection done at that point, which meant I only had to manually seek out around 80 more items.

To find the items you missed, I recommend first using this site to find out the name of the item you're looking for, then searching this thread to find its location.
You must be a member of the forums to search through the thread's posts.

If for some reason the thread above does not have the item you're searching for, a quick Google search will often come up with a source for the item's location. Just be sure to add in "Katamari Forever" to filter out all the unrelated results.

The most (if not only) frustrating item in the game will be the Cowbear, who runs at high speed around the Cows and Bears level. The main challenge of this item is reaching a size big enough to catch it (7.8m) as there is no eternal mode available. A more in-depth guide on Cowbear can be found here.

(You need 100% of the collection for this trophy, but this guide only deals with the most difficult item, which is the dreaded Cowbear)

This is the best Cowbear guide that I found. He plays on classic mode until he gets over 8 meters, and then waits in a certain spot to dash and grab cowbear.

Some guides have you get to a certain size, and then charge some guys to knock them out of the way, and then get to a bigger size just so you can charge cowbear. That sounded too complicated for me, which is why I like this video, because you don't have to charge anybody else first.

Watch the video and copy it as close as you can. You will probably mess up here and there and roll up a cow or bear too early. Soon you will have the route memorized and maybe tweak it to make it a little better for you. I went much slower than him (I didn't dash at all, except at the end for cowbear), and still had over 3 minutes left at the end.

So go slow, and don't worry at all about time. Make up your mind before you try for this that you will be patient and not get frustrated when you fail to get cowbear on your first 5 or 10+ tries. This ended up being a lot easier than I expected, but it did take me a couple hours. Good luck!