This trophy is for rolling up all the presents in the game.
Presents appear on every level. You can see which presents you have at the level select screen.
You must successfully complete a level in order for rolled up presents to count. It's easiest to do this on Eternal mode (which many levels have as an option).
I used this guide from Katamari on the Web to find the ones I missed through normal play:https://katamariontheweb.jcink.net/index.php?showtopic=199