So... is Beelzebub finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 25, 2012
Manga finished: March 13, 2015
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
Beelzebub centers around Tatsumi Oga, the strongest delinquent at a school full of delinquents. His life takes a bizarre turn when he's chosen as the caretaker of Baby Beel, the son of the Demon Lord.
Now, Oga is stuck with a baby demon and his demon maid, Hildegard. They must navigate the chaotic environment of Ishiyama High while trying to raise Baby Beel.
Oga faces the constant challenge of dealing with other delinquents and the strange situations that arise from having a demon baby. The series explores his attempts to manage his new role as a foster parent in the most unlikely of circumstances.