Like Generation V, Pokémon X & Y have brought several new battle types to the fold. However, at this time, these battles are only avilable within the confines of the singple player with no option to duplicate it within multiplay. This page is to detail those types of battle
Sky Battles are a new battle mode that only certain trainers will partake in. Within these battles, you can only use a select sort of Pokémon. For these battles, you have to use Flying-type Pokémon, or Pokémon with Levitate. However, even not all of those are candidates with Pokémon such as Doduo and Pidgey being exempt. Mega Charizard X can still be used in these battles despite not having the qualifying factors after Mega Evolving
Within these battles, you are also unable to use moves such as Gravity. However, other than those restrictions, the battles are largely the same to single battles in the game.
List of Pokémon that are exempt:
Horde Encounters are a new kind of wild Encounter where a horde of Pokémon appear and challenge you. These Pokémon can be anything from a group of one species of Pokémon, to a conglomeration of a couple that work togehter such as Miltank & Tauros, or who turn on eachother such as Seviper & Zangoose. These battles typically have the Pokémon at a significantly lower level so as to not overpower you, but it is essentially one-sided, requiring moves which take out the entire field to be at hand. You can cause them to occur by using Honey or Sweet Scent
All multi hit moves are calculated as if you're in the middle of a triple battle, but with two enemies at your side rather than allies. You can only capture Pokémon after you have defeated four of the five.
Inverse Battles are a brand new type of battle, located only in one house within Route 18. Once a day, you can challenge this man to a battle, but the battle rules are always contrary to standard. If a move is typically super effective on your Pokémon, it won't be very effective and vice versa, so you need to make sure to plan ahead if you are going to partake.