So... how the hell can you beat a Vaporeon?
Let's just say it's not going to be easy. Remember, Vaporeon is the 13th most powerful Pokémon in the game, which means there are 12 others that are potentially strong enough and suited to defeat it. The only problem is, unlike Vaporeon, these 12 Pokémon are either difficult to attain or -- in the case of Mew, Mewtwo, and the three Legendary Birds -- so rare that they haven't even appeared in the game yet. However, some players suggest relatively rare Pokémon like Snorlax or Lapras as your best bet.
Some have also suggested using strong Grass types, like Victreebell. We've also heard of cases in which a Venusaur smacked down a Vaporeon with its Solar Beam attack, so it's probably not impossible to beat them by other means if your Pokémon of choice is similarly powerful. One thing is certain, though: you'll never find out if you don't try. Good luck.