There are 50 Trophies that can be collected.

BRONZE

Taste of Victory
Win an event (no teams)

Red Carpet
Take a locked shortcut

Career is GO!
Complete the first championship of your career

Career 25%
Complete 8 different championships in your career

Career 50%
Complete 15 different championships in your career

Your Friends are Cool
Complete a championship in your career in a splitscreen team

Internet Famous
Win an online event (no teams)

Fish in a Barrel
Use power-ups against 3 drivers who are within range of the safety car (globals not included)

Heavyweight
Affect 3 drivers with a single Pulse

Fully Automatic
Hit the same driver three times with a 3x Ricochet Bubble

Scientific Method
Make an impact with each type of power-up

Nailed the Jump
Trigger a jump boost

Jump Boost Expert
Trigger 50 jump boosts

Slipstreamer
Slipstream past a driver

Slipstream Expert
Slipstream past 50 drivers

Shortcut Expert
Take every shortcut in the game

Abu Dhabi Expert
Win an Abu Dhabi event at 3,000cc (no teams)

Australia Expert
Win an Australia event at 3,000cc (no teams)

Belgium Expert
Win a Belgium event at 3,000cc (no teams)

Brazil Expert
Win a Brazil event at 3,000cc (no teams)

Germany Expert
Win a Germany event at 3,000cc (no teams)

Great Britain Expert
Win a Great Britain event at 3,000cc (no teams)

Italy Expert
Win an Italy event at 3,000cc (no teams)

Japan Expert
Win a Japan event at 3,000cc (no teams)

Monaco Expert
Win a Monaco event at 3,000cc (no teams)

Singapore Expert
Win a Singapore event at 3,000cc (no teams)

USA Expert
Win a USA event at 3,000cc (no teams)

Qualifying Lap
Set a Time Trial record

Bronze Time
Earn a bronze Time Trial record on all tracks

Player of Games
Complete one event in each race mode

Causing Trouble
Hit another driver after being eliminated

Ecto-won
Beat a friend's Time Trial lap

Prince of the Screen
Reach King of the Screen level 3

Social Butterfly
Complete one event with each constructor

Pitmaster
Repair in the pits 10 times

SILVER

Career 75%
Complete 23 different championships in your career

Shelf Promotion
Fill your career trophy cabinet

Around the World
Win an event on every track at 3,000cc (no teams)

Silver Time
Earn a silver Time Trial record on all tracks

Exhibition Rush
Earn 1,000 Exhibition points in under 5 seconds

Vapours
Win a Refuel event with an empty tank (no teams)

My House
Own the whole track in Sector Snatch

Shakedown
Make a nearby driver drop 600 points in Trophy Chase

King of King of the Screen
Reach King of the Screen level 6

Bingo!
Use a power-up against every opponent on the track (globals not included)

GOLD

Career 100%
Complete 30 different championships in your career

Gold Time
Earn a gold Time Trial record on all tracks

PLATINUM

Race Star
Unlock all 49 trophies

2 SECRET

BRONZE

Whoops!
Hit yourself with your own Ricochet Bubble

SILVER

They See You Rollin'
Earn 3,141 badges

http://www.ps3trophies.org/game/f1-race-stars/trophies/