It varies. Take a few just in case and make sure you weaken it first. If you need to you can run and come back later with more balls.
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You need 21 ultra balls to catch Heatran
depends on how weak he is and how lucky you are
You don't need a specific Pokeball. Try Dusk balls (If it is at night), Quick Balls (Very early in battle), Timer Balls (Late in battles), and Ultra balls after you have weakened it. Master balls could also catch it.
Arceus has a catch rate of 3, so you need LOTS of Ultra Balls. If you have a Master Ball, you can easily catch it. He is ridiculous, because it takes so long to catch him! I recommend master balls!
If you participated in the event, you can pick up the liberty ticket at the Pokemon center. Then you go to the last harbor in Castelia city and ride the boat to Liberty island. You fight a few members of Team Plasma, then you have the opportunity to catch Victini. The event is now over. If you did not get the event you may need to wait and hope that Nintendo does another.