There are 31 Trophies that can be collected.

BRONZE

Take Your First Steps
Play your first solo dance

Step Up!
Play your first dance battle

Just The Two Of Us
Play your first dance partners routine

Start Groovin'
Get a 5 star rating on 5 beginner, normal length routines

Two Left Feet
Get a 0 star rating on a beginner, normal length song

Sing While You Swing
Get at least a 'cool singing' rating in 5 performances

Dance Of Love
Perform a dance partners routine on St. Valentine's Day

Dancing The Night Away
Play a song late at night

The Camera Loves You
Save 10 video highlights

A Partners Production
Create a dance partners routine

It's Good To Share
Upload a video or snapshot highlight to the community gallery

Are You Cupid?
Heart 20 different videos or snapshots in the community gallery

We Like To Party
Play a 5 round party

School's In Session
Complete a section of any routine in dance class mode

Dance Director
Create a solo dance routine

Don't Sweat It
Perform a dance workout

SILVER

Grooving On Up
Get a 5 star rating on 5 intermediate, normal length routines

Streaker
Achieve a 70 move streak in any routine (excludes Creator Routines)

Millionaire
Accumulate 1,000,000 points

Stay On Target
Reach the Kcal target in every song of a single workout

We Are Party People
Play 20 party rounds in total

Class Act
5 star 20 sections in dance class

Teacher's Pet
5 star 50 sections in dance class mode

Hi-Score Hero
Get 40 hi-scores

This Is My Song
Get a 5 star rating on any professional, normal length song

GOLD

Dance Fever
Play 50 dances

Perfect Partner
Get a 5 star rating on 5 dance partners, normal length routines (excludes Creator Routines)

You've Got The Groove
Get a 5 star rating on 5 professional, normal length routines

Let It Burn
Burn a total of 1000 Kcals in Dance Workout

Dedicated To Dance
Dance for 10 hours in total

PLATINUM

DanceStar Superstar
Unlock all other trophies

http://www.ps3trophies.org/game/dance-star-party-hits/trophies/