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Catch Sword Art Online
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Credit for Summary: SAO: Alicization Wikipedia with many changes by yours truly.
A flashback occurs showing when the Administrator is losing her own memory space. She uses a child to link their memory. This was a fatal mistake of the Administrators as it means the child gets the same authority and power.
The child realizes this (who is revealed as the Cardinal of the great library) and so, she attacks the Administrator. She flees to the one out of two places the Administrator doesn't have authority over, the great library. There, she spends the last 200 years thinking of a way to defeat the Administrator and finds Kirito and Eugeo in the process.
While conversing with Kirito, the Cardinal explains how to get an Integrity Knight's memory back. Thus, the Cardinal allies with Kirito and Eugeo to defeat the administrator and get back Alice.