No exact number is required. It's just... luck.
From a mathematical perspective, you will need to reset 8,192 times in order to get a shiny legend (or, just a shiny, anyway) but it's chance.
It's like the game picks a number out of a hat. If it's not the 'shiny' number, then the Pokemon won't be shiny. And in the hat, there are 8,192 pieces of paper, with only one of them being the shiny number. (Do you get that? xD) There's no exact number of times until you pick out that shiny number. It could take a million tries until you find one! :o
It should also be noted that a normal shiny and a legendary shiny has the exact same chance of being shiny - except for the ones in Gen 5 and Gen 6, which are shiny locked.
Hope I helped. :)