C rank requires a total of 1,000 BP earned through ranked matches. You earn roughly 50 points on the lowest rank, and it only goes up with the higher ranked foes you face. This means if you have a friend with the trophy already willing to help out, the process could go a bit faster. If you are looking to boost it with somebody else, it is advised one of you gets the C rank and passes it to the other as you lose BP when you lose fights. On your way to this achievement, another will pop at 500 BP. C rank is the highest you need to rank, so once you obtain this you no longer have to partake in ranked matches!
Side note; best to do this while going for the arcade fight requests as they also count as ranked matches. Will save you some time to simply work on both and make progress towards each rather than simply play standard ranked matches THEN do fight requests.