You don't necessarily have to beat the elite four to catch any event pokemon, especially since the only way to get Arceus right now is to hack it.
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you do not necesarely have to beat the elite 4 to get arceus mostly because you can only get it via hack.
You can only get Shaymin, Darkrai, Manaphy and Arceus if you have beaten the elite four. You also need a national dex before you can go after any of them. Hope I helped.
It could be easy if you have a LV100 arceus shiny and when you beat all the elite in Pokemon dimond, pearl or platnium change arceus into fighting type and K.O. Cynthia.(only if you can)
You have to beat the Elite Four again.
No you can trade anytime before beating the elite four.