There are 12 Trophies that can be collected.

BRONZE

Complete Beginner's Course
Complete STAGES 1 and 2.

Intermediate Runner Certificate
Complete STAGES 3 and 4.

Polished Running
Perform at least five ground tricks before completing the course.

Hop! Step!
Perform at least five jump tricks before completing the course.

Acrobat Star
Perform at least three air tricks before completing the course.

Acrophobia!
Complete the course without jumping once.

What's the rush?
Perform at least 10 Ram Air Dashes before completing the course.

SILVER

Advanced Runner Certificate
Complete STAGES 5 and 6.

For the Birds
Perform at least fifteen trick combos before completing the course.

Model Runner
Receive at least a bronze medal on all courses.

Superior Runner
Receive at least a silver medal on all courses.

GOLD

Legendary Runner
Receive a gold medal on all courses.

http://www.ps3trophies.org/game/aero-cross/trophies/