There's no official mission or event in Pokémon Crater that involves Battle Arena Competitions.
Here are some possibilities you might be thinking of:
* A Fan-Made Event: Maybe you're thinking about a fan-made game or mod that features this kind of competition?
* A Future Game Feature: It's possible that future Pokémon games could introduce battle arenas or competitions in a Crater-themed location.
* A Misunderstanding: Perhaps you're thinking of a different game or a different location?
If you can provide more details about what you're looking for, I can help you further! For example:
* What kind of Pokémon game are you thinking about?
* Are you looking for a specific kind of competition?
* What is your goal in this hypothetical mission?
Let me know, and I'll try my best to answer your question!