So... is Shin Hikari Shinwa: Palutena no Kagami 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
Shin Hikari Shinwa: Palutena no Kagami presents a series of short stories expanding on the world of Kid Icarus: Uprising.
Each episode seems to focus on different aspects and characters from the game.
We can expect tales centered around the menacing Thanatos, the vengeful Medusa, and even a comedic look at the divine Palutena's less-than-stellar cooking attempts, all likely exploring their roles and motivations within the overall narrative.
The shorts aim to provide further insight into the game's universe and its inhabitants, offering viewers a deeper connection to the world of Kid Icarus.