From RWP Wiki
The T.T. Amulet is a collectible item in Diddy Kong Racing and its remake, Diddy Kong Racing DS. There's a total of four pieces of the amulet, with each one found inside each of the four battle arenas of Timber's Island.
The player has to win in each of the battle arenas to get a piece of the T.T. Amulet. Of course, to enter the battle arenas, the player has to find a hidden key, which can be found in some of the race tracks.
If the player gets all four pieces of the T.T. Amulet, he/she can enter the T.T. door that's inside Future Fun Land. However, the player must also collect 47 balloons during the process. Inside the T.T. door is a door leading to the second race against Wizpig.
In Diddy Kong Racing DS, the T.T. Amulet is won much differently. The player must find a key to make the Wish Door open. After entering the door, he/she will be able to draw his/her own track (although each track has the same theme) and then race T.T.. After beating him, the player will be given a piece of the T.T. Amulet.