The Regis is probably the easiest Pokemon in this game to shiny hunt, no soft reset required. Just one shot them everytime till you get a shiny. If you have Pokemon that are not Lv.100, it is a great way to level up, while looking for a shiny.
The reason it is so easy is when you beat them the statue you fight goes dormant and you just have to light up the pattern for them to fight them till you get a shiny. It is faster that way than soft resetting, I heard. Obviously you get it faster if you have a shiny charm, of course.