All you need to get this achievement is net at least a bronze medal in each of the time trial circuits. If at any point the timer goes down to zero on the bronze timer, you lose.
I had zero difficulty passing all of the tracks before the Hard difficulty where there is a very steep spike in difficulty. Don't be surprised if you have to retry the Hard tracks a few times before you nail them.
A good gauge for determining if you should just restart the race is if you slip into a silver timer at any point during the first lap and a half, restart the race. This may seem annoying but is better than the alternative of not realizing that you're going too slow until you're on the last lap.