Shedinja is all you need, Bro.
Kyogre is a tough Pokemon to counter, due its overwhelmingly high stats in the right places; it's practically invincible. If you use Shedinja, then no attack used by the common Kyogre will hit it.
Zapdos just can't out-muscle Kyogre. Yes, 100% Thunder is pretty awesome, but Kyogre would just use Ice Beam or Blizzard and OHKO Zapdos. For a legendary bird attempt, you could using the ever-so-bulky Articuno to stall it out with Toxic and/or Swagger, maybe.
There are probably other ways you could approach the Kyogre, but I'll others have a shot at this.