There are 12 Trophies that can be collected.

Bronze

Hell, LLC.
Take the Soul Train to Hell.

A Play of Infinite Acts
Save Bosco from his own personal hell.

Toy Production Manager
Save Santa from his personal hell.

Broadcast TV Executive
Save Grandpa Stinky from his own personal hell.

Say My Name
Stop the conception of a new hellspawn.

Chiptune Rockstar
Help Chippy prevent Hell from owning his soul.

Forbidden Brew
Prevent Stinky's from carrying Fruit of Knowledge Cider on tap.

Motivational Work Environment
View all the seven motivational posters in the Hell, LLC offices.

Pimp Le Car Great Reaping 5000
Receive all DeSoto decals in this episode by completing all levels in "Pimp Le Car Great Reaping 5000" and gather all bonus decals.

Silver

Office Snoop
Spy on Satan berating the staff each time the efficiency drops.

The Three Lords of Hell
Thwart the Lords of Hell's plan for world domination.

Gold

What's New, Beelzebub?
Complete Episode 5: What's New, Beelzebub?

http://www.ps3trophies.com/forums/ps3-trophy-news/4258-sam-max-beyond-time-space-episode-5-whats-new-beelzebub-trophy-list.html