There are 13 Trophies that can be collected.

BRONZE

APE TV is back on air
Complete the first studio of the Story Mode

Funzini Makeover
Complete the Story Mode

And the winner is
Win every mini-game once

Candy Store
Win every round of the story mode with Papa Funzini

Posh House
Win every round of the story mode with Mama Funzini

Casino Palace
Win every round of the story mode with Granny Funzini

Sheriff's Office
Win every round of the story mode with Billy Funzini

Toy House
Win every round of the story mode with Bella Funzini

Made of Bronze
Obtain all bronze medals in the Challenge Mode

SILVER

Steal the show!
In a 4 player Story Mode game, win every round

Made of Silver
Obtain all silver medals in Challenge Mode

Made of Gold
Obtain all gold medals in Challenge Mode

GOLD

Quite a feat!
Obtain all in-game awards

http://www.ps3trophies.org/game/lights-camera-party/trophies/