There is 6 track variants for each 9 maps. With 4 car classes equals 216 tracks you have to achieve gold. Make sure you unlocked every car from the Career mode. If you don't know which car to use go to the leaderboard and pick the same car as the guys who achieved the best times. Set the game to 15 laps, when you manage to get gold you can always press Back to end the race. Try to keep track of the maps you completed since there is no sign in the menu that says if you got the gold medal or not. But if you go in a track and in the upper-right of the screen you see names instead of just a gold medal time then it means you already did this. The lower the car class the slower and harder they are to control so try to start with Apex to hone your skills and get used to all the map variants.
Layton Raceway tips:
The Layton Raceway is easily the hardest level to achieve gold in time trial. For every vehicle classes use the last type of vehicles. The best strategy is to drift around the corners by holding LT+A. When drifting, try to stay on the pale gray part, it slows you down if you drive on it but it makes you a lot faster when you drift on it, and don't use the shortcut on the shortcuts variant, do the same thing as you did without it. The 2 upper vehicle classes are easier to achieve gold but the N-Dura and Evo GT will give you hell, patience is a virtue!