If you prefer to watch videos instead of reading the guide, feel free to do so. There is a video that covers every trophy on my YouTube channel. If you'd like and subscribe or even become a member, it would mean a lot to this channel!
The first and at this point only available cup to race in, is the Seasons Cup. It is pretty easy and offers perfect opportunities for trophies like Comeback King and Winning by the Book. You should try to win every race to minimize the cleanup later.
The second cup doesn't have any tracks with special trophies, but it is recommended to attempt some of the combat-related trophies during this step. If you need any further information on these, please take a look at step 4.
The Pulse Racer Cup is the third and final championship. It offers two racetracks with special trophies tied to them.
You may have unlocked some of these trophies already during the first three steps. However I clustered them here, because we need to start a few more races which gives us an opportunity to go for the missing ones.
Even though most of the combat-related trophies require some luck, there is a fair chance that you didn't need to do 25 races for them + all 3 cups. In this case you should be missing at least Supercharged at this time.