From my experience there are typically 6 common methods for shiny hunting. I’m going to order them from “easiest to encounter a shiny” to “most tedious to find a shiny”, assuming that the time period remains the same for each category, based on my own personal experience.
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Friend Safaris. From personal experience I can tell you that you are far more likely to run into a shiny here and you generally have more control over what nature the Pokemon in question has by leading with a Synchronizer. It isn’t easier because the rate of shinies is increased there, it just takes far less time to find an encounter, run from it, and then find another in comparison to the other methods. The one downside here is that if you’re looking for a specific Pokemon, you’re going to want to prepare yourself for finding one of the other 3 (or 2 if you’re hunting before completing the 6th gym) Pokemon before the one you’re looking for. But it still motivates me when I find one of the others because at least I’m not putting in hours of running around for nothing.
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Static encounters. These include things like Hidden Grotto Pokemon, a number of Pokemon that can be interacted with in the overworld and then battled, etc. These are also nice because you can control what nature the Pokemon you’re trying to catch has and you’re guaranteed to get the Pokemon you’re looking for when you find a shiny, unlike the Friend Safari. However, because this method requires you to soft reset after every failed encounter, it is more time consuming when it comes to encountering a shiny than the Friend Safari method.
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In-game trades. Trades from NPCs in Insurgence are not locked in terms of stats, nature, shininess, etc. so it is possible to obtain shinies from them. The upsides to this method are that some of the Pokemon in this category are exclusive and cannot be obtained through any other methods. The downsides are that firstly you cannot control the nature of the Pokemon you receive from the trade and it also is more time consuming than the static encounter method because you’re required to pass through a bit of dialogue and then a trade screen animation before being able to see if the traded Pokemon is shiny, then reset if not. This is about on the same level of tediousness as the starters but it does seem like it has taken me longer on average to obtain shiny starters in comparison to traded Pokemon. For the most efficiency here, you’re logically going to want to lead with the Pokemon you want to trade in your party to reduce time between soft resets considerably.
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Starters. This is relatively similar to static encounters except that you have to go through a fair amount of dialogue, a nickname screen, and then wait for YOUR Pokemon to be sent out before being able to soft reset. It requires a bit more concentration here over the other methods simply because selecting “Yes” on the nickname screen takes more time and can result in you filling the nickname area with m’s without noticing. Obviously the upsides here are getting shiny Delta starters while the downsides are again being unable to control nature and needing to focus a bit more.
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Eggs. I suppose it’s debatable whether or not this is more tedious than the next on the list, though on average your likelihood of obtaining a shiny here is higher. Unless you’re absolutely infatuated with breeding a certain Pokemon competitively and then having it also be shiny, I would stick to Friend Safaris, with an exception being made for the Mysterious Egg in the Ancient Tower. You’ll need to save before picking up the egg and then you’ll also need to leave your location and Fly or Teleport to Vipik City in order to see the guy who sells the egg hatching chemical. My times for this procedure starting from the Ancient Tower take somewhere between 40-45 seconds between resets, so while it is usually more efficient than the next on the list, it is far behind the rest in terms of both time per reset and concentration needed for maximum hunting efficiency.
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Pokepon. Now, I will preface this by saying that your odds of getting a shiny from Pokepon are higher than running into one in the wild, which includes all of the methods listed above (1/2400 versus 1/8192 chance). But this is for one encounter, with each encounter occurring at best once every 20 minutes. Simple math tells you that using any of the other methods during that same 20 minute period is going to end up producing a higher chance of finding a shiny. So the only scenario where this method is more advantageous than the rest is if a) You have enough time to find one encounter per 20 minutes (and then bike around to hit the additional ~1500 steps requirement) but not enough time to spend those 20 minutes continuously searching for a shiny either through encounters or resets or b) The Pokemon in question is an event Pokemon which otherwise is not available as a shiny and also is not available in the wild. To put this into perspective, I’ve probably spent an average of at least 6-8 hours per day for at least 2 months and still have not succeeded in Pokepon’ing a shiny Delta Misdreavus or Munchlax; at most the other methods (mainly trades and starters) have taken a little over a week for the same amount of time on average, though I am also still trying to get a shiny out of that Mysterious Egg. An additional downside here is that Pokepon’s nature change feature may potentially ruin a Pokemon that you aim to use competitively.
Note: The guide above was written before 1.2’s release, Dexnav and Deino mission were added in 1.2 and hence are listed separately.
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Dexnav. Open Dexnav, scan for the pokemon you want, search in wild grass/water/cave by biking/running, run away if it’s not shiny and repeat till you find it. It doesn’t have chaining, it’s a flat rate that applies for each encounter when scanned. This means that even if the player leaves the area, the rate isn’t affected. You’ll need to have the pokemon registered in your pokedex by having caught one before and the continous switching between mouse and keyboard is a bit tedious but otherwise, it’s has the most chance for shiny.
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Broadcast Tower Mission 5 - Deino. While not a shiny hunting method per se, it deserves a special mention since the Deino encountered during this mission is always shiny. Another thing is that the three ‘roaming’ legendary beasts have a chance to overwrite the deino encounter meaning you have a chance of getting one of the beasts as shiny per save. Just save infront of the Deino after unlocking the beasts and catching two, and soft reset till you get the third beast as a shiny. However you wouldn’t get the shiny deino if you do that.