There are 15 Trophies that can be collected.

Bronze

Hero of Alena
Arcade, Planets – Complete planet Alena

Hero of Sekora
Arcade, Planets – Complete planet Sekora

Hero of Mahler
Arcade, Planets – Complete planet Mahler

Hero of Werth
Arcade, Planets – Complete planet Werth

Hero of Yuriko
Arcade, Planets – Complete planet Yuriko

Scrooge MacBoom
Arcade – Get 10 special weapons

The Tokenizer
Arcade, Planets – Collect 15 tokens with a single boost

Shield Blaster
Arcade, Planets – Collect 5 shield tokens while already having a shield

Crushing
Crush – Complete mode

Slick
Disc Slide – Get 10x multiplier

Bombs Away
Orbit Bomber – Get 1000000 points

Hot Roller
Rock & Roll – Get 50x multiplier

Core Destroyer
Trucker – Destroy 30 green cores

Silver

Multiplier Hero
Arcade, Planets – Get 20x multiplier

Gold

Hero of the Galaxy
Arcade – Complete all planets

http://www.ps3trophies.com/forums/playstation-trophy-news/10899-super-stardust-delta-trophy-list.html