Bronze

Dinner Time!
Trophy won for completing the 'Prosciutto's Strange Recipe' quest.

Close Call
Trophy won for completing the 'Replay's Trials and Tribulations' quest.

Rock Solid Defense
Trophy won for completing the 'Attack of the Unicorns' quest.

Sous Chef
Trophy won for completing the three missions in the 'Prosciutto's Strange Recipe' quest.

The Big Escape
Trophy won for completing the three missions in the 'Replay's Trials and Tribulations' quest.

Untouchable Stronghold
Trophy won for completing the three missions in the 'Attack of the Unicorns' quest.

Perfect Rescue
Trophy won for completing the three missions in the 'Saving Koolo Max' quest.

Silver

Maxi-Rescue
Trophy won for completing the 'Saving Koolo Max' quest.

King of Challenges
Trophy won for completing the 20 standard challenges.

Champion of Chance
Trophy won for winning 10 random challenges.

One For All and All For One
Trophy won for completing at least one quest with each of the 8 playable characters.

Gold

Maxi-Minimoys
Trophy given for having unlocked all the quests, the playable characters, the mini-games and the bonuses.

Source