Yes, there were many events giving them away.
The parts of a normal Arceus that are white turn yellow in the shiny form. This is true no matter what plate it holds.
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A shiny Arceus does exist in the game's coding however it is not possible to legitimately obtain it since Arceus' event item was never released. Arceus is not the only Legendary that you cannot get as a shiny as most new legendary Pokemon in recent games are coded to never appear as a shiny. Even though they won't appear as a shiny they still have the data for it to prevent glitches in the game's system.
Shiny Arceus is impossible to obtain without participating an event or using a cheating device, for it is shiny-locked. Shiny locking prevents certain Pokemon to have the shiny PID, and a legendary being shiny (like Celebi, Mew, and Keldeo) isn't legal.
u can with an Action Replay
it is the rarest shiny ever in history only one even close to that is shiny arceus
no i tried before