Memory Spheres are a recourse that allow you to instantly clear a level in Campaign Mode or Daily Challenge as long as you have previously completed that level with a star ranking of three.
You will use one Memory Sphere and the amount of energy required to clear the level when instant clearing a stage.
After you have used the Memory Sphere you will receive all items you would have received if you were to have normally cleared the stage.

How to get memory spheres?

Memory Spheres can be bought from the store
You get them each day after completing all Daily Challenges.
As a reward for won fight.