Complete all career missions.
There are 53 missions in total and you'll need to get at least one cup in each for them to count as 'completed'. You get one cup for third place, two cups for second place and three cups for first place, meaning you'll need to finish at least third in every mission. There are also bonus cups in some missions for completing objectives such as killing a certain amount of enemies or earning a certain amount of points. For the time attack missions you'll need to achieve at least the slowest time on the list but realistically you will need at least 138 cups to unlock the final boss mission which is required for this trophy and then you'll get 3 cups for completing that, meaning the least amount of cups you can technically get is 141.