Kyogre is simple. It's not subtle. It is a water type with a huge special attack stat that sets up rain with its ability, and with powerful water attacks like Water Spout and Origin Pulse. As a result, it is fairly predictable. But predictability and a poor speed don't stop it from being one of the most powerful pokémon in the game, because when played right anyone can turn out at the wrong side of a devastating Water Spout.
Kyogre @ Blue Orb
Ability: Drizzle
EVs: 252 Def, 252 Special Attack, 4 Speed
Modest nature
- Water Spout
- Origin Pulse
- Ice Beam / Thunder
- Protect
Essentially THE Kyogre set you'll usually see in the Ultra Series. Primal Reversion might not benefit Kyogre quite as much as it does for Groudon, but the access to primal weather is necessary in an environment where Primal Groudon is popular to give Kyogre the ability to remove extreme sunlight. This allows it to force out Groudon under threat of it losing a lot of health bars at once to Water Spout, and often allows it an opening to get Water Spout off, or just nuke Groudon if the opponent doesn't have any pokémon left to switch in. Origin Pulse is there as your water attack if your health goes down, and Ice Beam is often preferred over Thunder to get a better hit on Rayquaza and to have a move left to hit Primal Groudon if extreme sunlight is in effect, leaving other team members (like Ludicolo or Tapu Koko) to deal with enemy Kyogre and Tapu Fini threats.
There are some alternatives it can run. I ran Z-Psych Up in the Moon series to allow it to copy a Xerneas's Geomancy boost and get a simultaneous full heal for maximum Water Spout damage as Kyogre with a Geomancy boost is capable of planet-destroying feats, but having to sacrifice the Blue Orb for it isn't worth it for the Ultra Series. Regular Psych Up can still be considered if your other legendary is Xerneas, however Xerneas isn't quite as popular in Ultra Series as it was in the prior series, so it's a bit too situational for copying enemy Xerneas boosts. Plus, it's difficult to find space on Kyogre's moveset for it and having to be in play next to your boosting Xerneas leaves it a bit match-up dependent.
Scald is sometimes used as a reliable single-target option to bypass Wide Guards, but is also difficult to find space for on the moveset.
As for partners, Tailwind support is quite vital. Tailwind allows Kyogre to spam Water Spout much more freely as it isn't particularly fast normally, otherwise it always has to worry about taking damage from its opponents before. Tornadus, Crobat, Salamence, Lunala, they can all set it up. In the Sun and Moon series, Araquanid is a very interesting partner for Scarf Kyogre. Essentially, you use a U-Turn Incineroar to get Kyogre in safely and then use Entrainment on Kyogre (aiming for Incineroar) in that same turn. Effectively, Kyogre safely comes in after enemy attacks, sets up rain with Drizzle, and then immediately gets Drizzle replaced by Water Bubble, allowing it to then use its Scarf to spam Water Spout at twice the normal power, essentially classifying Kyogre as a weapon of mass destruction. Araquanid also hits hard under rain with Liquidation even without investment, offers Wide Guard support, and can even steal berries with Bug Bite or set up Sticky Web, and is also very bulky with a Wacan Berry. Unfortunately it's a combo that doesn't work quite as well in Ultra Series because you'd lose the rain from Kyogre if it loses Primordial Sea, and flying damage is actually more of a concern there with Mega Rayquaza and Mega Salamence being around.