You’ll need it for specific evolutions.
If you want to evolve all your Pokemon in Pokemon Legends: Z-A, then you will need to track down all manner of items. The Shiny Stone is one such item, and this is where you can get your hands on it.
Check out our POKEMON LEGENDS: Z-A INTERACTIVE MAP.
How to get the Shiny Stone in Pokemon Legends: Z-A

To get the Shiny Stone, you can visit the Stone Emporium to the west of Vert Sector-9, on the main street that runs directly north. You will need to visit after Main Mission 39, as you will not get access to a Shiny Stone in the Stone Emporium until then. You will just have to hope you run into one as world loot.

The good news, at least, is that there does appear to be a guaranteed Shiny Stone spawn. Play until after Mission 5, then go to the Cafe Gallant. If you go as far as Nouveau Cafe, then you have gone too far. You will find a Holovator on the building to the west of it. Once on the roof, head all the way around in a large half circle to get to the walkway that goes across the top to the next building. Go there and drop down into the courtyard to find a Shiny Stone.
There are three Poke Balls down here with different items in them, so grab them all. Once you have your Shiny Stone, you can use it to evolve Floette into Florges and Roselia into Roserade.
For more guides and news, be sure to check out our Pokemon Legends: Z-A page
