There are hundreds of Pokémon that you can capture in Pokémon Go around the world. You encounter these creatures in several ways, from completing the small tasks you receive on Pokéstops, defeating them in raids, entering special events, or just searching the world. Many of these Pokémon have unique statistics tied together, so not every Pokémon you catch will be the same. You also have the chance to find a glossy version, which is a unique colored Pokémon that you will find extremely rarely. Ledyba is a Pokémon that you can have all over the world, and there is little chance of catching a shiny version.
The glossy version for Ledyba is not very different from its usual version. The overall shading of the Pokémon looks a little brighter and its usual orange and yellow coloration is accentuated. You may not be able to say that you came across a shiny version of this Pokémon until there are significant sparks around it that every shiny Pokémon will make when you find it.
The chances of capturing the glossy version remain the same as with all other standard Pokémon. You have a chance to find one of the 500 shiny Ledyba, so it may take you quite a while to finally meet the shiny one. When you do and develop it into Ledian, it stays shiny. Shiny Pokémon has no better statistics. The only thing that is special about him is her appearance.