Yes, you can catch the shiny version of Tapu Fini in Pokemon GO following its addition on May 9, 2023.
After beating a 5-star Tapu Fini Raid, there is a 5% chance that the Tapu Fini you encounter will be the ultra-rare shiny version. This is the standard shiny odds for Legendary Pokemon in Pokemon GO.
If you are hunting for a shiny Tapu Fini, there’s no better time to catch one than the Pokemon GO Tapu Fini Raid Hour. This is because the number of Raids featuring this Legendary Pokemon will be greatly increased then.
Of course, to get a shiny Tapu Fini, you will likely have to defeat this Legendary Pokemon over a dozen times. Make sure you know how to get more Raid Passes so you can keep battling until you catch the shiny!

What Color is Shiny Tapu Fini?
The shiny version of Tapu Fini is black and white with blue hair. The black body and white pattern remain the same as the standard version, but the purple of the standard version is replaced by black for its shiny counterpart.
This black color scheme is especially cool as it matches the shiny versions of all of the other Legendary Tapus:

Tapu Fini is just one of the dozens of Legendaries in the game. Check out our list of every Legendary Pokemon in Pokemon GO to find out which ones have shiny versions.