First, I'm going to cover some details on how shinies even work in this game so we're all on the same page.
How the shiny rate works
The base shiny rate is 1 in 4096. When a Pokemon is spawned in, the game "rolls" RNG to determine if it's shiny. By default, it'll roll 1 time, but there are two ways you can increase the number of rolls per Pokemon:
- Owning the Shiny Charm (reward from Mable) permanently gives + 3 shiny rolls
- Using Sparkling Power donuts in Hyperspace Distortions (DLC)
- Lv. 1 gives +1 shiny roll
- Lv. 2 gives +2 shiny rolls
- Lv. 3 gives +3 shiny rolls and guarantees a shiny (more on this later)
This means that the best odds you can have is 7 rolls (1 by default + 3 from Shiny Charm + 3 from Lv. 3 Sparkling Power), which is about a 1 in 585.57 chance.
The exception is that Pokemon revived from fossils always have a 1/4096 rate no matter what. If you really want a shiny fossil Pokemon, they can rarely show up as wild spawns in the DLC via special scans, at which point you can use all of the methods mentioned here.
How spawning works
The basic idea behind all shiny hunting methods is that you want to repeatedly despawn and respawn ("reroll") the Pokemon you're looking for until it gets spawned in as a shiny.
Pokemon usually spawn in when you get within about 50 units away from them, and despawn when you get beyond about 70 units away from them, though it's not always easy to tell exactly how far away you are. You can drop a pin on your map to view the in-game distance units.
Triggering a loading screen despawns everything. Flying to a Fast Travel point, transitioning between day and night, going through certain buildings, blacking out, starting up the game after it was closed, and going through a distortion are some examples of actions which do this.
Up to 10 wild shiny Pokemon at a time are preserved and given immunity to despawning, so you usually don't need to worry about your shiny getting overwritten if you reroll the area again. This means that you don't need to check for shinies after every single reroll of the area. If you spawn in an 11th shiny Pokemon, the game will despawn the oldest uncaught shiny, but this shouldn't be a concern unless you've intentionally ignored 10 shinies instead of catching them...
By the way, if you get rid of the Pokémon in any way—fainting it, catching it, or scaring it away—it will need a set amount of real life time somewhere in the range of 2-5 minutes in order to respawn again and you won't be able to reroll it until it comes back. So try to avoid doing these actions since they'll slow down your shiny hunt. Unlike in some previous games, building a streak of KOs has no benefits.
Check out this map to see where all the different spawns are!
With that information in mind, here are some of the methods for hunting for shinies!
Fast Travel method
- Repeatedly fly to a Fast Travel point.
This is a very straightforward method. Since everything was unloaded when you went on the loading screen, the game will have to generate a new set of Pokemon when you reappear. Remember that Pokemon spawn in if they're within 50 units from you! There is a Fast Travel point by every Wild Zone and in every distortion, so there are a lot of desirable locations. Traveling to the entry portal while inside a distortion has the advantage of a shorter loading screen.
You can automate this method if you know how to use a third-party controller that lets you schedule a series of actions (i.e., controller macros). Otherwise, you just have to execute them manually.
Bench method
- Repeatedly sit at a bench.
This is similar to the Fast Travel method, just with triggering the day/night transition screen by killing time at a bench instead. Benches are all over the city, and they're especially useful if you want to hunt a rooftop spawn.
The advantage of this method is that it can be automated if you have a third-party controller with a "turbo" function that lets you repeatedly input a button press by holding the button down, which is easy to buy online. You can then use an elastic band or some kind of small wedge to hold the control stick down while your controller continuously inputs A to sit at the bench over and over again.
Wild Zone 3 stairs method
- Repeatedly run up and down the stairs on the tower in Wild Zone 3.
This also triggers a loading screen, so it works the same as the last two methods.
This method is really easy to pull off automatically without any special tools, since you can just wedge something against the control stick to hold it down and cause you to run up and down the stairs over and over again. The disadvantage is that it only works in this one specific area.
Run back method
- Repeatedly run into and out of the range for a Pokemon to spawn (50 units) and despawn (70 units).
In this method, you're basically running laps at a certain distance away from your target to repeatedly run close enough to spawn it in and then run away from it until it despawns. You don't need to have a clear line of sight to do this. Holovators can help you traverse the distance more quickly.
This method can be finicky for several reasons. For one, it isn't always easy to tell if a Pokemon has despawned, since they can be invisible but not actually unloaded, or to tell how far away you are from a Pokemon, especially since they might move around. Another downside is that it takes some concerted effort to execute. It might also be hard to find a clear path where you can easily run back and forth.
Notably, this method is useful for hunting the 5 special scan legendaries in the DLC.
Lv. 3 Sparkling Power (DLC only)
- Enter a distortion with Lv. 3 Sparkling Power active to find a guaranteed shiny.
The first Pokémon that matches the type on your Lv. 3 Sparkling Power will run the usual shiny rolls, and if none of them are successful, the game will rewrite its ID to make it be shiny. Therefore, as long as the distortion contains spawns of a matching type, you're guaranteed to find a shiny! Typically, this will be a spawn that's near the entry portal, so it unfortunately doesn't work on the special scan legendaries.
See my answer here for more information about using donuts for shiny hunting.
Spawn overload method (Patched)
- Exploit a glitch that causes extra Pokemon to be spawned.
This method was patched out of the game in version 2.0, so it only works on older versions. Since it isn't useful to most people, I won't put a detailed explanation here, but I think it's worth documenting. Basically, there was a bug that would cause more Pokemon to be spawned than there are normally supposed to be, and more spawns mean you have better odds when hunting using another method like Fast Travel or bench resetting. For instance, instead of 2 Alpha spawns in the middle of Wild Zone 20, you could have 3 or more at a time.
Here is a video demonstrating the method if you want to learn it in detail.