So... is Tattoon Master finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: August 23, 1996
Manga finished: April 01, 1997
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
Hibio's life takes an unexpected turn when his adventurer mother returns from a research expedition with a rather unusual arrangement.
She's promised him in marriage to Nima, a beautiful young woman from a mysterious tribe.
Without his knowledge or consent, Nima arrives in Tokyo, ready to be his wife.
The culture clash between Nima's magical heritage and Hibio's ordinary Tokyo life creates comical and chaotic situations.
The anime focuses on the humorous challenges they face as Hibio adjusts to having a sudden bride with a vastly different background.