SpongeBob SquarePants Underpants Slam!

There's no way to keep track of which characters you've beaten the game with, so the easiest way to do it is all in one go. Beat the game with SpongeBob and get all bronze medals at the same time, then beat it with Patrick and get all silver medals, and again with Mr Krabs and get all gold medals. Finally you'll have to beat all 9 levels again with Sandy and Plankton, so go through each one systematically with both and providing you've beaten every level with every character, the achievement will unlock.