Successfully complete one of the following tasks to get a trophy:

10 times Wild Draw Four (Bronze): When you use the Wild Draw Four Card 10 times in tournament.
2 times Wild card in a game (Bronze): When you use the Wild Card 2 times in a round in tournament.
Win 10 matches (Bronze): When you win a total of 10 matches in tournament.
Challenge UNO (Bronze): When you successfully catch someone forgetting to call UNO in tournament.
First UNO (Bronze): When you first call UNO in tournament.
First win (Bronze): When you win a round for the first time in tournament.
Challenge Wild Draw Four (Bronze): When you successfully challenge an illegal use of a Wild Draw Four Card in tournament.
Finish 10 games (Bronze): When you complete 10 rounds (win or lose) in tournament.
5,000 points! (Bronze): When you reach 5,000 points in Tournament play.
Play online (Bronze): First time you play a round online.
Invite your friend (Bronze): First time you invite your friend to play with you.
Win 10 games online (Bronze): Win 10 online UNO rounds.
Play 50 games online (Bronze): Play 50 online UNO rounds.
Win game without drawing cards (Silver): When you win a round without drawing any cards in tournament.
Top 50 in the world (Gold): Check the leaderboard when in the TOP 50.