Conformation of the full list from: http://www.ps3trophies.org/game/smash-cars/trophies/

Bronze

Demolition Master   
Hit 15 objects in any single player level (original content). You must earn a bronze medal or higher in order to unlock the trophy.

Air Time Expert   
Get 75 seconds of air in any single player level (original content). You must earn a bronze medal or higher in order to unlock the trophy.

Star Collector   
Accumulate 270 stars in single player mode using your best score from each level (original content).

Trickster   
Complete 15 air tricks in any single player level (original content). You must earn a bronze medal or higher in order to unlock the trophy.

Lap Champ   
Beat all base lap times in every single player level (original content).

Race Ace   
Beat all base race times in every single player level (original content).

Smash Cars Superstar   
Get 30 stars in one single player level (original content). You must earn a bronze medal or higher in order to unlock the trophy.

Bronze Champion (Hidden)   
Earn a bronze medal, or better, in every single player level (original content).

Silver

Smart Driver
Find all the shortcuts in every single player level (original content). You must earn bronze medals or higher in order to unlock the trophy.

Safe Driver
Complete all single player levels without crashing or using any respawns (original content).

Silver Champion    (Hidden)
Earn a silver medal, or better, in every single player level (original content).
 
Gold

Gold Champion (Hidden)
Earn a gold medal in every single player level (original content).