This trophy is for rolling up all the cousins in the game.
Cousins appear on every level. You can see which cousins you have at the level select screen.
You must successfully complete a level in order for rolled up cousins 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=194