So... is Battle Girl High School finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
In the year 2045, the world is under threat from mysterious beings called Irousu, forcing humanity into containment.
Hope lies with the "Hoshimori," ordinary girls attending Shinjugamine Girls Academy, who are destined to fight back.
The anime follows a training program at this academy, where the girls learn to harness their potential and combat the Irousu to reclaim Earth.