You start MR2 off as Trainer Rank 1. To get to the next Trainer Rank, you must beat an official tournament.
Trainer Rank 2 = D Tourney Trainer Rank 3 = C Tourney Trainer Rank 4 = B Tourney Trainer Rank 5 = A Tourney Trainer Rank 6 = S Tourney Trainer Rank 7 = Beat any Major-4 battle Trainer Rank 8 = Beat another M-4 battle Trainer Rank 9 = Beat another M-4 battle MASTER Rank = Beat the last tournament left out of the four