There are 51 Trophies that can be collected.

Bronze

Arts and Crafts    
Construct 10 Engineering Items     

Tinkerer    
Construct 50 Engineering Items

Jetpacker    
Kill an Authority Enforcer during Jetpack descent     

Silent But Deadly    
Stealth kill 10 Enemies with the Striker Crossbow     

Hat Trick    
Kill at least 3 Enemies with a single Mind Controlled Enemy     

Decapathon    
Get 10 Headshot kills with the Wingstick     

Open Minded    
Get 10 Headshot kills with the Sniper Rifle     

Jumper    
Perform all 18 Vehicle Jumps     

Gotta Have 'Em All    
Collect all Playing Cards on one play-through     

Master Chef    
Collect all Recipes and Schematics in one play-through     

Hardest Deck    
Beat Teague's hardest Deck     

JACKPOT!    
Roll 4 Targets in the first round of Tombstones     

Just a Flesh Wound    
Complete the final round of 5 Finger Filet     

Deliverance    
Complete the final round of Strum     

Minigamer    
Win all Minigames 

Lead Foot    
Win a Race in the Campaign

Demolition Man    
Destroy 100 Enemy Cars     

It's Good!    
Score each of the 3 Field Goals from the ATV     

Roadkill    
Run over 10 Mutants     

Ghost Buster    
Complete Ghost Hideout in the Campaign     

Waste Management    
Complete Wasted Garage in the Campaign     

Gladiator    
Complete Mutant Bash TV in the Campaign     

It's Alive!    
Complete Dead City in the Campaign     

Wellness Plan    
Complete The Well in the Campaign     

Debunked    
Complete Shrouded Bunker in the Campaign     

ytiC daeD    
Complete Dead City Reverse in the Campaign     

Jail Break    
Complete Authority Prison in the Campaign     

Vault Assault    
Complete Gearhead Vault in the Campaign     

Power Struggle    
Complete Power Plant in the Campaign     

Decrypted    
Complete Jackal Canyon in the Campaign     

Mutie Blues    
Complete Blue Line Station in the Campaign     

Bringin' Home the Bacon    
Earn 750 Dollars in one episode of Bash TV in the Campaign

Dev Graffiti    
Find the secret Developer Graffiti Room

The Legend Begins…    
Complete a Legend of the Wasteland     

Anthology    
Complete all Legends of the Wasteland

No Room for Sidekicks    
Complete a Legend of the Wasteland without any player(s) becoming incapacitated     

Fresh Meat    
Complete a public Road RAGE match     

MVP    
Get first place in a public Road RAGE match

Silver

Passive Aggressive    
Get 3 kills with a single Sentry Bot     

Three Birds, One Bomb Car    
Kill 3 Enemies with one RC Bomb Car     

Keep 'Em Coming    
Get 5 kills with one deployed Sentry Turret     

Mechanocide    
Kill 100 Enemies with Sentry Bots, Sentry Turrets, or RC Bomb Cars

Rage Cup    
Win all Races in the Campaign

Mr. Oddjob    
Complete 5 Job Board Quests in one play-through

Hurt me plenty    
Finish the Campaign on at least Normal difficulty     

Ultra-violence    
Finish the Campaign on at least Hard difficulty     

RAGE Nightmare    
Finish the Campaign on Nightmare difficulty

A True Legend    
Complete a Legend of the Wasteland on Nightmare difficulty

Gold

Hey, not too rough    
Finish the Campaign on any difficulty

Obsessive Compulsive    
Reach 100% Completion in the Campaign

Platinum

Master of the Wastelands    
Earn all 50 Trophies

http://www.ps3trophies.org/game/rage/trophies/