Here is the full list of all 38 The Voice trophies - there are 24 bronze, 9 silver, 4 gold and 1 platinum.
Played and completed every song
Completed all exercises with the Voice Coach
Completed all "Expert" exercises with the Voice Coach
Completed all "Advanced" exercises with the Voice Coach
Completed all "Basic" exercises with the Voice Coach
Completed all "Warm-up" exercises with the Voice Coach
Progressed from the Blind Auditions with all four coaches turned
Won The Voice with two different coaches
Completed five coach challenges
Won The Voice
Made it to the Final of The Voice in Season
Progressed to the Semi-Finals in Season
Got the public vote for the first time and progressed to the Quarter-Finals
Progressed to the Final 12 in Season by being in your coach's final three
Progressed from the second Battle Round in Season
Won both Battle Rounds in Season
Won and progressed from the first Battle Round in Season
Played Season for the first time
Got eliminated from The Voice in Season
Completed your first song
Unlocked all trophies in The Voice
Completed a two-player duet
Started a Season in Duet mode
Played a song in Voice Party
Got your only "I Want You" in the last three pages of a song
Had all four coaches "I Want You" on four separate occasions
Completed ten coach challenges
Completed all sixteen coach challenges
Completed five unique songs with more than 90% average technique
Completed ten unique songs with more than 90% average technique
Completed fifteen unique songs with more than 90% average technique
Completed twenty unique songs with more than 90% average technique
Progressed from the Blind Auditions with one coach turn
Progressed from the first Battle Round in Season with a Steal
Chose a new coach after receiving two or three Steals after one performance
Progressed from the second Battle Round with a Coach Steal
Made it to the Live Playoffs in Season after two Coach Steals
Won The Voice with four different coaches