In Pokemon Legends: Arceus, Arceus is a legendary Pokemon.
In the game, Arceus' capture is the final quest (main mission). Obtaining it requires completing most of the endgame, particularly Quest 26: you must have the Azure Flute.
The Azure Flute must be obtained after completing Quest 26, an intense confrontation between Giratina and Volo (one of the most difficult confrontations in the saga).
You must capture all 237 of Hisui's main Pokemon. It's not enough to register them, you have to capture them.
It is not necessary to capture Phione, Manaphy, Darkrai, or Shaymin. Whenever you want, you can complete these quests (acquiring them will result in you having 241, Arceus as your final Pokémon, 242 out of 242).
It is difficult to fight Arceus, but it is not impossible. It will start like the encounters with Noble Pokémon, with real action and a stance bar that you will need to break with Balms before facing him in turn-based combat.
The elemental type of Arceus can be changed once it has been captured. Using the Legend Playe that you acquired during your adventure in Pokemon Legends: Arceus, Arceus can adopt any of the 18 elemental types. Use the Dragon Plate from the item inventory if you want it to be a Dragon type.