I had a really long, detailed answer, but by computer crashed ;~;
Super Battles are the upgrade from the normal battles. For example, there are Single Battles and Super Single Battles. Super Battle format is unlocked by defeating the Battle Chatelaine at the end of the regular battles. Super Battles go for an infinite amount of rounds (or 1000, I'm not sure), with matches against Battle Chatelaines every 50 rounds.
Chatelaine means "the woman in charge of a large estate". The Battle Chatelaines are the headmistresses of their respective formats. They do not appear outside of their specialty, with the exception of Multi Battles. The Chatelaines are as follows:
Nita – Single Battles
Evelyn – Double Battles
Dana – Triple Battles
Morgan – Rotation Battles
On a side note, you can battle two Chatelaines at once in Multi Battles. You'll fight Dana and Evelyn in regular Multi Battles and Nita and Morgan in Super Multi Battles
For the Pokémon and movesets of the Battle Chatelaines, look [here.]
There are two aspects of th Battle Maison that involve Wally. The first is Multi Battles. In Multi battles you can either fight alongside a nearby player, an AI of someone from your friend's list, or one of four NPCs: your rival (Brendan/May), the Team boss of your game (Maxie/Archie), Steven Stone, or Wally. Wally's Pokémon will be:
- Leaf Blade
- Close Combat
- Swords Dance
- Psycho Cut
Magnezone@ Air Balloon
- Flash Cannon
- Light Screen
I'm not 100% positive that Magnezone has dual Screens, so correct me if I'm wrong.
The second thing that has to do with Wally happens when you reach 50 consecutive wins in any format of the Battle Maison. You will be awarded a monument, and Wally will appear. After that you will be able to battle him.