There are 34 Trophies that can be collected.

Silver

Death Mode: Hills n' Spills
Complete the Death Mode level.

Death Mode: Sparkle Darkle
Complete the Death Mode level.

Death Mode: Sneak n' Deke
Complete the Death Mode level.

Death Mode: Rowdy Cloudy
Complete the Death Mode level.

Death Mode: Thermogenica
#1 Complete the Death Mode level.

Death Mode: Thermogenica
#2 Complete the Death Mode level.

Death Mode: Mechanica
Complete the Death Mode level.

Death Mode: Aquatica
Complete the Death Mode level.

Death Mode: Extraterrestria
Complete the Death Mode level.

Death Mode: Disasteroids
Complete the Death Mode level.

Death Mode: Galaxanoids
Complete the Death Mode level.

Death Mode: Invaderoids
Complete the Death Mode level.

Death Mode: Break-a-noids
Complete the Death Mode level.

Death Mode: Purgatory #1
Complete the Death Mode level.

Death Mode: Purgatory #2
Complete the Death Mode level.

Death Mode: Event Horizon #1
Complete the Death Mode level.

Death Mode: Event Horizon #2
Complete the Death Mode level.

Death Mode: Cities
Complete the Death Mode level.

Death Mode: Touch The People
Complete the Death Mode level.

Death Mode: Spiral Staircase
Complete the Death Mode level.

Beat School: Straight Up
Complete the Beat School level.

Beat School: Tiny Groove
Complete the Beat School level.

Beat School: Hi-Hat Spice (not very spicy)
Complete the Beat School level.

Beat School: Lullaby
Complete the Beat School level.

Beat School: Chord Tweak
Complete the Beat School level.

Beat School: Chordaby
Complete the Beat School level.

Beat School: A Rolling Frolic
Complete the Beat School level.

Beat School: It's Getting Tense In Here
Complete the Beat School level.

Gold

Campaign Complete
Complete all Campaign levels.

Platinum

You've Gone Platinum
Complete all Death Mode and Beat School levels.

http://www.ps3trophies.com/forums/playstation-trophy-news/20481-sound-shapes-trophy-list.html