Here is the full list of all 6 Grand Prix Story trophies - there are 1 bronze, 3 silver and 2 gold.
Proof that Kairobot joined the team
Proof of continuing to improve speed for many years.
Proof of winning the Grand Prix.
Proof of developing S-rank vehicle.
Proof of collecting more than 25 types of parts.
Proof of developing the first vehicle.