EDIT: Here's the list of super effectives each uses if you playing against the diamond version set.
Mewtwo: Flamethrower
Lugia: Aeroblast
Kyogre: Ancientpower (irrelevant if it's choice band locks it into another move but Mysterial WILL switch out if he has to)
Palkia: Ancientpower
Latios: Shadow Ball
Manaphy: No super effective moves, but if it's using rest/hydration it can take a while to beat with shedinja's low attack power and it will make toxic stalling pretty useless, if shedinja has to use struggle the recoil ends it for you. Make sure you use shedinja's Heal Block move (level 52) or hope you have good enough accuracy with fury cutter to get it's damage high. Or just switch out the weather and revert to toxic stalling.
The way I won was sending out Shedinja/Palkia, I then switched out manaphy to dialga to absorb the laughably weak ancient power his Kyogre got locked into and then just ignored manaphy till the end when I could let shedinja heal block and fury cutter away. If you do this though make sure nobody on you team has ice weakness cause Manaphy will spend most of the time you ignore it Calm Minding up it's stats, once it starts ice beaming you can survive 2 hits if your lucky and iof all the threats to shedinja aren't gone by then the whole strategy is useless. The team I used was Shedinja, Palkia, Kyogre, and Dialga.