There are 27 Trophies that can be collected.

Bronze

Raw Rookie
Play a ranked game online

From Downtown
Score 50% of your team's points while only shooting three pointers

Finger Roll
Make 5 layups in a row without getting blocked

He's on Fire!
Hit a buzzer beater while on fire

Burning
Keep yourself or your teammate on fire until it exhausts by making 5 or more unanswered baskets

Wrecking Crew
Beat Backboard Smash in under 2 minutes

Silver

First Time for Everything
Win a ranked game online

Start to Finish
Win an online ranked game while leading after each quarter

Iron Will
Break the backboard in a Classic or Remix game with an alley oop!

Mojo
Win a game with a layup buzzer beater

Double Up
Beat the CPU by doubling their score in a Classic 2v2 or Remix 2v2

Atlantic Division Represent
Defeat the Atlantic Division Legend Team in Classic Campaign

Central Division Represent
Defeat the Central Division Legend Team in Classic Campaign

Northwest Division Represent
Defeat the Northwest Division Legend Team in Classic Campaign

Pacific Division Represent
Defeat the Pacific Division Legend Team in Classic Campaign

Southeast Division Represent
Defeat the Southeast Division Legend Team in Classic Campaign

Southwest Division Represent
Defeat the Southwest Division Legend Team in Classic Campaign

Eastern Conference Division
Face the hidden boss after Classic Campaign with a team from each division in the Eastern Conference

Western Conference Domination
Face the hidden boss after Classic Campaign with a team from each division in the Western Conference

Too Late
While losing by one point, go up for a game winning dunk and have time expire. You lose!

Gold

Rolling
Win 10 ranked games online

Clean Sheet
Win a Classic or Remix game without letting the opposing team score

3 The Hard Way
Beat the Beastie Boys in Remix Campaign

Triple Up
Beat the CPU by tripling their score in a Classic 2v2 or Remix 2v2 game

Classical Campaign
Defeat the hidden boss after completing Classic Campaign

NBA Domination
Face the hidden boss after Classic Campaign with a team from each division

Platinum

BOOMSHAKALAKA!
Unlock all other Trophies

http://www.ps3trophies.org/game/nba-jam/trophies/