Escalation Battle is a stage in SMSB.
It appears to be set in the distortion world. The gimmick of this stage is the level ups. You can level up on this stage, which boosts youre attack, speed, and defense. To level up, you have to do enough damage to the stage attraction, Giratina. Giratina spawns at the start of the battle, and won't leave. Giratina tries to attack fighters by ramming into them, launching tornado like projectiles, and dissapeering and reappearing to hit a fighter. (Like it used Shadow Force) Giratina is not aggressive, but as fighters levels grow, he gets more agressive.
The stage is based off of a special stage in Pokemon Shuffle, where you fight Giratina, Cresselia, Latias, Latios or Darkrai depending on the event. Each time you beat them, the stage level goes up, and the pokemon becomes harder, as well as the catchability increasing.