Arceus form usage differs depending on level on the ladder. This Arceus usage data is from the higher Ubers ladder.
Arceus-Normal
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Free to hold any item and provides STAB and priority with Extreme Speed
Arceus-Ghost
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Takes care of the numerous Psychic and Ghost types in Ubers
Arceus-Water
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Easily handles the likes of Blaziken, Ho-Oh, and Groudon.
Arceus-Fairy
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Useful due to the ridiculous amount of Dragon types in Ubers, but there are also many Steel type threats.
Arceus-Grass
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Mainly used for coverage against Kyogre, which few Ubers-mons can handle.
Honorable Mentions:
- Arceus-Rock- quickly counters Ho-Oh and Reshiram and also offers a typing which is otherwise non-existent in Ubers.
- Arceus-Poison- can absorb Toxic, allowing it to set up. However, there are many Ubers Pokemon that resist or are immune to Poison type moves
- Arceus-Ground- Earthquake is ridiculously powerful, especially with a Swords Dance boost and made extremely useful now that Mega Mawile and Aegislash are banned to Ubers
- Arceus-Steel- Can provide a Physical or Special set with an immunity to Toxic, allowing it to set up
Source