After you finally defeat Giratina, you receive the Azure Flute and a final mission.

Seek Out All Pokémon

You will need to have caught pokémon 001 through 237 in your pokédex before you can proceed (it's not enough to have only seen them).

If you view the "Entire Hisui Region" tab of the Pokédex, and press Y to sort it by Ordered Numerically, you will see question marks for the entries that you have not yet seen, and pokémon that you have seen but not caught will have a grey picture. In addition, you can press Y to sort by Research Level to see which pokémon you have seen but not yet caught. Use this method to find out which pokémon you are missing, such as evolutions that you have not yet evolved, and so on. Completing requests may also help you see pokémon that you haven't seen yet.

Play the Azure Flute

When you have caught pokémon 001 through 237, go to the Summit Camp in the Coronet Highlands, and go northeast to the Stone Portal. Enter the cave and go through it. Go to the platform at the end of the temple and you will be asked if you want to play the Azure Flute. Say yes, and if you have caught pokémon 001 through 237 in your pokédex, Arceus will appear.

Battle Arceus

Throw balms throughout the battle whenever you can, to reduce Arceus's health bar. Run away from the glowing circles on the ground, and dodge to jump over the energy rings that come from Arceus. When Arceus makes a glowing orb appear above its head, repeatedly dodge to the side to avoid getting hit by the beams of light that shoot out of it.

Arceus will teleport to a side of the area. Go close to Arceus to avoid the glowing red area of the floor.

Arceus will disappear and create a rift, and will dash across the area out of the rift, so dodge to the side to avoid getting hit.

If Arceus starts glowing, with multiple orbs around it, hit Arceus repeatedly with balms until the orbs disappear. If you do not remove the orbs quickly enough, Arceus will use a powerful attack. If you do remove the orbs, Arceus will be stunned. Use a partner pokémon to battle the level 75 Arceus. It will change its type throughout the battle and use super-effective moves on your pokémon, so bring a full party of pokémon that are level 75 or higher. After you defeat it, throw as many balms as you can.

Afterward, you get the Legend Plate, and Arceus. Congratulations!