Diddy Kong Racing

Since each boss has to be beaten twice, there are different ways of telling. If you have won the first race:
-Wizpig will be on his door, and touching it will give a prompt telling you to beat the Silver Coin Challenges.
-Entering a track will start a Silver Coin Challenge.
If you have beaten the boss a second time:
-Taj's face will have replaced Wizpig's on the boss door.
-All the track doors have two Gold Balloon's pictured, as you have beaten both the regular race and the Silver Coin Challenge.
-The trophy race will be playable.
-You will have earned a piece of the Wizpig Amulet, which you can see by talking to T.T. or by seeing how much of the Wizpig face on the Timber's Island has changed from stone to colored.

Hope that helps!