While Pokémon Stadium 2 does have a storyline, progress in the game can be made by winning Cups in the Stadium and completing the Gym Leader Castle. When all Cups have been won and the Gym Leader Castle completed, the player's Rival will appear. Defeating the Rival will unlock Round 2, in which the player must re-challenge the Stadium, Gym Leader Castle, and the Rival in order to complete the game. But, they have different Pokémon and the difficulty is much higher.
Stadium:
The player begins by choosing 6 different Pokémon. There are 250 different Pokémon to choose from; including some legendary Pokémon. Pokémon tournaments take place in the Stadium. There are four Cups to participate in. Each round consists of eight battles, and every Cup except the Little and Prime Cup consists of four rounds, named after Poké Balls, that must be cleared to win that Cup.