Is it possible to be the same level as perpetua when she learns the ability to see your level and scans you?
Not without cheating, no. While you can theoretically min-level by running from some fights and save-scumming to ensure you never fail the roll, there are too many essential battles where you can't run and have to defeat the girl you're fighting to progress, which gives you exp.
Don't quote me on this, but bare minimum you would need to fight: Perpetua 1-->Perpetua 2--> Ancilla--> Shizu 1--> Nara-->Aiko and Feng--> Shizu 2-->Himika or Mizuko at least. And even assuming you're able to pull through with your severely under leveled character, the amount of exp you'd gain from beating all the aforementioned above would send you soaring past level 10 or whatever low level Perpetua is.
