There are 30 Trophies that can be collected.

Bronze

Perfectionist – Bronze
Finish any song with 80% "Good" or "Perfect" moves.

Constellation Maker – Bronze
Get at least 1 star on every choreography in the "Songs" tab.

Just Dancer – Bronze
Play 10 songs.

Sweat Me a River – Bronze
Earn 1000 Sweat Points.

Eyes Wide Shut
Get 5 stars on any song after disabling pictograms in the options menu.

Highway to the Stars
Get 5 stars on 2 songs in a row (excluding Speed Shuffle & Simon Says).

Stylist
Get 5 of the 7 different styles.

Marathon – Bronze
Play 5 songs in a row on Non-Stop Shuffle.

Light Speed
Play 20 songs in a row on Speed Shuffle.

On Fire!
Perform well enough to catch "On Fire!" during a song.

Magnificent Medley
Get 3 stars or more on 3 Medleys.

Get Mashed!
Get 5 stars on a Dance Mash-up song.

Silver

Perfectionist – Silver
Finish any song with 90% "Good" or "Perfect" moves.

Constellation Maker – Silver
Get at least 3 stars on every choreography in the "Songs" tab.

Just Dancer – Silver
Play 75 songs.
Sweat Me a River – Silver
Earn 10,000 Sweat Points.

Sweat & Score
Reach 400 Sweat Points with a 4-star rating on any song.

Ace Pair
Finish any Duet with 2 players getting at least 3 stars on both choreographies.

Shaky Simon
Get at least 1000 points on every "SHAKE" move on Simon Says Mode.

Marathon – Silver
Play 15 songs in a row on Non-Stop Shuffle.

Sweatin' Together
In a Free Session, finish a song with every player scoring over 300 Sweat Points for that song.

You're Golden
Perform 50 Gold moves.

Halfway There!
Collect 260 stars.

Gold

Perfectionist – Gold
Finish any song with 100% of "Good" or "Perfect" moves.

Constellation Maker – Gold
Get 5 stars on every choreography in the "Songs" tab.

Just Dancer – Gold
Play 150 songs.

Sweat Me a River – Gold
Earn 30,000 Sweat Points.

Big Band Theory
Finish any Dance Crew with all 4 players getting at least 5 stars.

Marathon – Gold
Play 30 songs in a row on Non-Stop Shuffle.

Platinum

Just Dance Legend
Earn every Trophy in Just Dance 3.

http://www.ps3trophies.com/forums/playstation-trophy-news/7593-just-dance-3-trophy-list.html