Sky battles are a battle type in generation VI that was not carried over into any generations after it. Sky Battles only exist in Kalos, and only Pokemon that can Fly or have the ability Levitate can participate. Although, not all Pokemon that have the ability to fly can participate in Sky Battles. Such as Hawlucha. Gengar cannot participate in Sky Battles, either, however, Gastly and Haunter, can. Certain attacks are banned from Sky Battles as well, such as Surf, Body Slam and Spikes.
What did you think of Sky Battles? I honestly despised them, and found them too limiting. Honestly, Hawlucha not being able to participate in Sky Battles is a bit dumb. I know it's shown on the ground, but honestly, any Pokemon that it stated to fly/float/levitate or is Flying type, should be allowed in a Sky Battle. Like, Magnezone is a Pokemon that floats, and yet it's not allowed in Sky battles, that's honestly also extremely dumb. It's a magnet, it can float in midair, and yet it's not allowed in Sky Battles? Stupid. Also SCYTHER can participate in Sky Battles, but it can't even learn Fly. Oh, yeah, and so can Combee and Vespiquen, along with Mantkye. Mantkye can't even fly or float in the air? So, yeah, that's another one.