39 battles: (78 teams):

Genesect...........32
Thundurus..........27
Bisharp............22
Heatran............19
Lucario............18
Garchomp...........17
Aegislash..........16
Deoxys-Speed.......16
Landorus-Therian...16
Rotom-Wash.........16
Tyranitar..........14
Azumarill..........12
Conkeldurr.........12
Pinsir.............12
Talonflame.........12
Venusaur...........12
Charizard..........11
Greninja...........11
Landorus...........11
Excadrill...........9
Latias..............9
Latios..............9
Kingdra.............8
Celebi..............7
Manaphy.............7
Dragonite...........6
Gardevoir...........5
Hippowdon...........5
Hydreigon...........5
Kyurem-Black........5
Diggersby...........4
Gengar..............4
Gyarados............4
Mandibuzz...........4
Raikou..............4
Skarmory............4
Zapdos..............4
Clefable............3
Gliscor.............3
Keldeo..............3
Mawile..............3
Politoed............3
Scizor..............3
Terrakion...........3
Tornadus-Therian....3
Wobbuffet...........3
Chansey.............2
Deoxys-Defense......2
Dugtrio.............2
Heracross...........2
Kabutops............2
Magneton............2
Smeargle............2
Suicune.............2
Victini.............2
Alakazam............1
Chandelure..........1
Ditto...............1
Empoleon............1
Espeon..............1
Magnezone...........1
Mamoswine...........1
Medicham............1
Mr. Mime............1
Ninjask.............1
Quagsire............1
Shaymin.............1
Vaporeon............1
Volcarona...........1