The game has 44 trophies that can be earned.

Bronze

Trofeo Rame
Achieve 1st place in the 348 Challenge Trophy Event.

Trofeo Ferro
Achieve 1st place in the 348 TB Trophy Event

Trofeo Perla
Achieve 1st place in the F355 Challenge Trophy Event.

Trofeo Topaz
Achieve 1st place in the F355 Berlinetta Trophy Event.

Trofeo Carnelian
Achieve 1st place in the 360 Modena Trophy Event.

Trofeo Tourmaline
Achieve 1st place in the 360 GT Trophy Event

Trofeo Mercurio
Achieve 1st place in the F430 GTC Trophy Event.

Trofeo Malachite
Achieve 1st place in the 550 Maranello Trophy Event.

Trofeo Acciaio
Achieve 1st place in the 575M Maranello Trophy Event.

Trofeo Bronzo
Achieve 1st place in the 575 GTC Trophy Event.

Trofeo Argento
Achieve 1st place in the F40 Trophy Event.

Trofeo Oro
Achieve 1st place in the F50 Trophy Event.

Trofeo Granato
Achieve 1st place in the F333 SP Trophy Event.

Trofeo Obsidian
Achieve 1st place in the FXX Trophy Event.

Trofeo Opale
Achieve 1st place in the 365 GTB4 Comp. Trophy Event.

Trofeo Platino
Achieve 1st place in the 512 M Trophy Event.

Trofeo Rubino
Achieve 1st place in the 512 S Trophy Event.

Trofeo Zaffiro
Achieve 1st place in the 250 LM Trophy Event.

Trofeo Smeraldo
Achieve 1st place in the 250 Tessarossa Trophy Event.

Trofeo Diamante
Achieve 1st place in the 250 GTO Trophy Event.

The Graduate
Complete Tutorial mode for the first time.

Italian Lap King
Beat the Lap Record on all Italian circuits in Time Trial mode.

Euro Lap King
Beat the Lap Record on all European circuits in Time Trial mode.

North American Lap King
Beat the Lap Record on all North American circuits in Time Trial mode.

Numero Uno
Achieve a pole position in a GT Race Series

Prancing Horse
Complete a GT Race Series.

First GT Race Series Win
Win your first race in a GT Race Series.

Double Whammy
Achieve 2 podium finishes in a Road GT Series.

The Veteran
Complete Expert difficulty in Arcade mode.

First Across The Line
Place first at every circuit in the game.

New Wheels
Buy your first car.

100 Wins
Win 100 races.

Silver

Hot Shot
Achieve 75% accuracy or above in all categories in Tutorial mode.

Time Trial Lap King
Beat the Lap Record on every circuit in Time Trial mode.

Road GT Racer
Win a race at every Road GT Series circuit.

Classics Race Ace
Win a race at every Classics Series circuit.

The Champ
Complete Legend difficulty in Arcade mode.

2000 On The Clock
Race a total of 2000 miles.

The Collector
Buy every car available in the game.

Gold

GT Race Series Star
Complete a GT Race Series with maximum points.

Road GT Series Star
Complete a Road GT Series with maximum points.

Classics Series Star
Complete a Classics Series with maximum points.

Arcade Gold
Achieve a gold trophy in every Arcade Mode Difficulty.

1 Secret

http://www.ps3trophies.com/forums/trophy-news/44155-ferrari-race-experience-trophy-list.html