How to unlock Kyogre
There is no direct purchase for Kyogre. It appears on the Hoenn banner inside the 5★ pool. The 5★ band takes 1.5% of all pulls and holds 103 partners, so one specific Kyogre works out to about 0.0146% per draw. The 70-pull pity counter guarantees a 5★, but it does not target Kyogre specifically, so a guarantee can still resolve to another 5★. A duplicate Kyogre refunds 300 coins at the 5★ rate.
Kyogre stats and rank
The sheet lists Kyogre at 115 HP, 116 speed, ×1.52 attack, ×1.25 physical and ×1.52 special, with 90 defense and 140 special defense — 670 base-stat total. On the three-stat percentile this is 87.0 out of 100, which puts Kyogre at rank 29 of 966 and in tier S. Relative standing explains more than the total here: its strongest slot is special multiplier (99th percentile) and its weakest is defense (73rd percentile), so it is a specialist rather than an all-rounder.
Best moves in Kyogre's pool
At move level 5 the pool is led by Body Slam at 75.6 damage per 0.71s (132.6 effective DPS, ×1.25 multiplier), then Tackle at 33.6 damage per 0.38s (112.0 effective DPS, ×1.25 multiplier), then Hyper Beam at 126.2 damage per 1.76s (108.9 effective DPS, ×1.52 multiplier). 5 of its 12 damaging moves scale with the physical multiplier and 7 with the special one, alongside 5 support moves. Its special multiplier is the higher of the two (×1.52 against ×1.25), so special moves convert better. The top option beats the second by 20.6 DPS, which decides slot one and leaves slot two as a judgement call.
Evolution cards for Kyogre
Its starting move, Water Gun, evolves into Scald once the move is at level 5 and you hold the Power card, which boosts attack for that run. If Power never appears in that run's level-up offers, the move stays at level 5 and unevolved. 12 of its 17 moves carry an evolution card, across 6 distinct cards (Vigor, Sprint, Power, Reflexes, Armor and Synthesis). The strongest of them is Body Slam at 132.6 effective DPS, so that is the one worth holding a card for first.
Kyogre compared to similar partners
The two closest stat lines in the roster are Reshiram (+0 HP, +0 speed, same attack multiplier, +10 total) and Lunala (+17 HP, +3 speed, -0.07 attack, +10 total). Against Reshiram, the two are level on speed and the two carry an identical ×1.52 attack multiplier, and the rank gap is 3 places. Those differences are what you actually trade when swapping partners, not a straight upgrade path, so neither side is a strict upgrade and the move pools have to break the tie.