Here is the full list of all 38 Just Dance 4 trophies - there are 20 bronze, 13 silver, 4 gold and 1 platinum.
Obtain All Other Trophies
Complete your First Song
Get 3 Stars on a Song
Get 3 Stars on 5 Songs
Get 5 Stars on a Song
Get 5 Stars on 5 Songs
Perform all Gold Moves in a Song
Perform all Gold Moves in 5 Songs
Perform only Good Moves or better in a Song
Perform only Good Moves or better in 5 Songs
Get a Perfect on the Last Move of a Song
Get 10 Perfect Moves in a row in any song
Complete a Song with 80% or more Perfect Moves
In any Dance Crew Song, All four Players Get 3 Stars or better (Four Coaches)
In any Dance Crew Song, All Four Players Get 5 Stars (Four Coaches)
Finish a Duet with 2 players getting 5 Stars on both Choreographies
Get 5 Stars on any Mash-Up
Complete 5 Dance Quests
Get 3 Stars on All Songs (No Alternate Versions, Mash-Ups or Battles)
Get 5 Stars on All Songs (No Alternate Versions, Mash-Ups or Battles)
Win a Battle
Win each Battle Once
Unlock an Item from the Wheel of Gifts
Complete a Sweat Class
Complete a full 10 Minute Sweat Class
Complete a full 25 Minute Sweat Class
Complete a full 45 Minute Sweat Class
Burn 500 Calories in Sweat Mode
Burn 1000 Calories in Sweat Mode
Burn 2000 Calories in Sweat Mode
Complete at least one Class from each of the 5 Sweat Programs
Dance to the Same song 3 times in a row
Get 5 Stars on a Song with Pictograms Disabled
Get 5 Stars on the Extreme Version of Wild Wild West
Dance to (I've Had) The Time of my Life Alone
Dance to We No Speak Americano with 3 others
Dance to Time Warp twice in a row
Win a Battle as the Never Gonna Give You Up Coach