It actually isn't the type of game to "complete", but well, got "S" rank on all Story characters and bought everything in the shop including hidden material, so in a way, it is complete. All that is left is to slowly enjoy the game?
But it really isn't that hard to get S in Story Mode. Just set the difficulty to Hard, play PuyoPuyo (old rules) for each stage, and make a simple 5-6 chain kind of like this (it's actually a little off here!):
Everything in store has been bought!