[The Damned]

In-game, anything works. It's simply a matter of leveling up enough. There are lots of people who have done Magikarp or Caterpie-only runs, where they don't use any other pokémon (except for HMS, but they aren't used for battle) and still beat the Elite Four.

Competitive battling... nope, not happening. There's a reason why tiers exist, and why most pokémon aren't in the higher ones.