There are 50 Trophies that can be collected.

Bronze

Milk the Cow    
Complete any song (Dance Mode)     

It's Electrifying!    
Perform 5 moves in a row with a Perfect rating (Dance Mode)     

Greased Lightning    
Achieve a 3 star rating for a Show Your Moves section (Dance Mode)     

I Got Chills…    
Achieve a 5 streak (Dance Mode)     

…They're Multiplying    
Achieve a 25 streak (Dance Mode)     

Dance Fever    
Achieve a x5 multiplier (Dance Mode)     

We Go Together    
Complete a song with both a dancer and a singer present (Dance Mode)     

Best of Show    
Win 10 rosettes (Challenge Dance Mode)     

Unbeatable    
Complete a game without losing or failing any challenges (Challenge Dance Mode)     

All The Right Moves    
Pass one of each challenge type (Challenge Dance Mode)

Rock and Roll Party Queen    
Complete all songs (Dance Mode)     

One For the Yearbook    
Have 20 photos taken of your performance (Dance Mode)     

Something's Begun    
Complete any song (Karaoke Mode)     

Vocal Superstar    
Achieve an x5 multiplier (Karaoke Mode)     

Tell Me More    
Hit all the spoken word notes in any song that contains them (Karaoke Mode)

Songbird Shake    
Complete all songs (Karaoke Mode)     

Full House    
Complete a song with two Dancers and two Singers (Dance Mode)     

Oldie But a Goodie    
Unlock a Classic Grease minigame     

Treasure Hunter    
Unlock half the Classic Grease minigames     

Master of Unlocking    
Unlock all the Classic Grease minigames     

Sandy's Songbook    
Unlock all songs (Dance Mode)     

Yearbook Yardstick    
Unlock all characters     

Greasy Tom    
Successfully sabotage 3 times in Greasers v Jocks     

All The Way Home    
Hit 5 consecutive home runs in Greasers v jocks     

Basket Case    
Make 5 consecutive baskets in Greasers v Jocks     

On Your Marks    
Complete a race without hitting any hurdles in Run For Your Love     

Road Hodge    
Complete Thunder Road Race without hitting an obstacle     

Let's Get Nuts    
Fully tighten 8 nuts in one playthrough of the Wheel Nuts microgame in Greaser's Garage     

Hit It    
Flatten 3 bumps in a row during Panel Beating in Greaser's Garage without causing any more arising     

Aint No Dropout    
Hit 20 consecutive moves in Beauty Sleep     

Band Leader    
Hit 20 consecutive moves in Rockin’ Rydell     

Gamesmaster    
Complete all the Classic Grease minigames     

T-Bird Trio    
Achieve a score above 250,000 on three Classic Grease minigames     

Buddy Lovin'    
Achieve a team score above 500,000 on three Classic Grease minigames     

Tap It    
Get high scores on all Classic Grease rhythm-action minigames

Silver

The Zuko    
Complete these moves with a perfect rating – Lightning Arm, Hydromatic Intro, Lasso (Dance Mode)     

The Kangaroo Bop    
Complete these moves with a perfect rating – Tell Me More Heart, One I Want, Shaky (Dance Mode)     

Greaser     
Complete these moves with a perfect rating – Grease Star, Tiptoe Clicks, Thrust (Dance Mode)     

Rock'n'Roller    
Complete these moves with a perfect rating – Jive Orangutan, Sue, Mid Swing (Dance Mode)     

Super Stepper    
Finish a song without performing any poor rated moves (Dance Mode)     

Dance Expert    
Finish a song with at least 75% moves rated Perfect (Dance Mode)

Angelic    
Finish a song without performing any poor rated phrases (Karaoke Mode)     

Singing Expert    
Finish a song with at least 75% perfect phrases completed (Karaoke Mode)

Minigame Mogul    
Get high scores on all Classic Grease minigames

Gold

National Dance-Off Champion    
Get high scores on all songs (Dance Mode)

Hopelessly Devoted    
Post scores to the high score tables for all songs while singing

Platinum

Love-in at the Drive-in    
Earn all the other trophies in the game

2 Secret

http://www.ps3trophies.org/game/grease-dance/trophies/