PokéBase - Pokémon Q&A
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  • Mew
  • Celebi
  • Jirachi
  • Deoxys
  • Manaphy
  • Phione
  • Darkrai
  • Shaymin
  • Arceus
  • Victini
  • Keldeo
  • Meloetta
  • Pecharunt

Meltan (and therefore Melmetal) can be caught in non-Cherish Balls in Pokemon GO, but I didn't include GO for any other Mythical and didn't want to make an exception here. Other side series and spinoff games are not included either.

Mythical Pokemon (Bulbapedia)

Hope I helped!

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I guess I'll add that there are glitches you can use to begin a battle with the Hall of Origin Arceus in D/P without hacks. You still may not consider that a legitimate process, though.
That's fair, I don't really know how legitimate glitches are to people.
Arceus can he obtained in other pokeballs from the 2013 event.