37 battles: (74 teams):

Genesect...........31
Thundurus..........24
Bisharp............20
Lucario............18
Heatran............17
Aegislash..........16
Garchomp...........16
Rotom-Wash.........16
Landorus-Therian...15
Deoxys-Speed.......14
Conkeldurr.........12
Pinsir.............12
Talonflame.........12
Tyranitar..........12
Charizard..........11
Greninja...........11
Azumarill..........10
Landorus...........10
Venusaur...........10
Excadrill...........9
Latias..............9
Latios..............9
Celebi..............7
Kingdra.............7
Manaphy.............7
Dragonite...........6
Gardevoir...........5
Hippowdon...........5
Kyurem-Black........5
Diggersby...........4
Gengar..............4
Gyarados............4
Hydreigon...........4
Mandibuzz...........4
Raikou..............4
Zapdos..............4
Clefable............3
Gliscor.............3
Keldeo..............3
Mawile..............3
Politoed............3
Scizor..............3
Skarmory............3
Tornadus-Therian....3
Wobbuffet...........3
Deoxys-Defense......2
Dugtrio.............2
Heracross...........2
Kabutops............2
Magneton............2
Smeargle............2
Suicune.............2
Terrakion...........2
Victini.............2
Alakazam............1
Chandelure..........1
Chansey.............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