Bronze

The Story Begins
Clear SPLASH HILL ZONE, ACT 1.

Crush Dr. Eggman
Defeat a boss for the first time.

The First Chaos Emerald
Acquire a Chaos Emerald.

Enemy Hunter
Defeat 1,000 enemies.

Golden Flash
Clear all Acts as Super Sonic.

All Stages Cleared!
Defeat the final boss and view the ending.

Contender
Upload your recorded scores and clear times for all stages.

Ring Collector
Collect all the Rings in 'Special Stage 1' and Clear the stage. 

Silver

Immortal
Build up 99 or more extra lives.

Super Sonic Genesis
Acquire all seven Chaos Emeralds.

Speed's My Game
Clear SPLASH HILL ZONE ACT 1 in less than a minute. 

Gold

Untouchable
Clear the E.G.G. STATION ZONE without taking any damage.

Source: http://www.ps3trophies.com/for…..-list.html