There are 7 Trophies that can be collected.

Bronze

Hooray for music!
For having played the whole Music Workshop, without skipping any activities in the Pause Menu.

Clear blue sky!
For having played the whole Sky Workshop, without skipping any activities in the Pause Menu.

Magician's apprentice!
For having played the whole Magic Workshop, without skipping any activities in the Pause Menu.

Silver

The little turtle!
The turtle game in Little PooYoo mode, without any mistakes from beginning to end (excl. tutorial).

The little clever rabbit!
The rabbit game in Little PooYoo mode, without any mistakes from beginning to end (excl. tutorial).

Gold

The clever rabbit!
The rabbit game in Big PooYoo mode, without any mistakes from beginning to end (excl. tutorial).

The super turtle!
The turtle game in Big PooYoo mode, without any mistakes from beginning to end (excl. tutorial).

http://www.ps3trophies.com/forums/trophy-news/62000-learning-pooyoos-episode-1-trophy-list.html