It's hard enough to find a Legendary Pokemon, let alone a Shiny one.
Acquring a Shiny Legendary Pokemon can be quite the task. Typically involving hours upon hours of soft resetting, it is often the most tedious grind. And for competitive players to get the correct IVs and shiny, the chance of that is almost impossible.
Note: This list is subjective and reflects only the opinion of the writer.
Top 5 Shiny Legendary Pokemon
#5 - Solgaleo
Both of the Sun and Moon legendaries have amazing looking Shiny sprites. However Solgaleo has the upper hand on this since it's main naturally looks like a sun, the color scheme just works perfectly for it.
Also it gets additional points for being easily obtainable. This was given out in Gamestops as a Mystery Gift.
#4 - Celebi
This is one of the first canonical Shiny Legendary Pokemon. In the newest Pokemon movie, Secrets of the Jungle, Celebi is found to be Shiny. Obviously in the last movie starring Celebi, Pokemon 4Ever, Celebi was it's regular color scheme.
Maybe since Celebi can travel through time, it's capable of soft resetting itself until it's Shiny. Although that's just a theory.
#3 - Kyogre
Pink Shinies are famous in the Pokemon community as some of the best looking Shiny Pokemon, and Kyogre is no exception. Kyogre's Shiny sprite is amazing since it differs so much from its original.
Shiny Kyogre is obtainable pretty easily in Pokemon Go during it's event. Surely, Pokemon Go will bring back the event for those who missed it the first time around.
#2 - Rayquaza
In the movie, Hoopa and the Clash of Ages, Hoopa calls upon the aid of this Shiny Rayquaza. It's color scheme just makes it much darker, which definitely makes it much cooler.
Rayquaza also has a great mega form, which the darker color scheme compliments greatly. It's showing in this movie is amazing and gives much more appreciation for it's Shiny form.
#1 - Mew
Unfortunately Shiny Mew can only be legitimately obtained in Pokemon Go during its event. Surely Game Freak will give it an encounter in a Pokemon game one day, through which players will be able to obtain it via soft resetting. But for now Mew's Shiny form will remain quite elusive.
Mew's Shiny form is amazing, with a vibrant sky blue color scheme. Mew remains the best Shiny Legendary so far.