Rarest Hunts
These shiny hunts are the only ways of obtaining some specific shiny pokémon, some of these hunts can take exceptional amounts of time, have incredibly low probability or a high likelihood of failiure. Very few have legitimately obtained most of these pokémon.
Mew
While not technically a "shiny hunt" or even "legitimate", shiny Mew can be obtained in any generation one Pokémon game through the use of glitches, through the use of a glitch called "Arbitrary Code Execution"(ACE) accessed through a glitch item "8F", a Mew's Determinent Values (DV's) may be changed so that it is shiny when transferred to newer generations, although this method is extremely dangerous and Mew's obtained in this way are still not perfectly legitimate so it is mostly avoided, (there is however an easier method for getting shiny Mew in generation three.)
Link to a video tutorial on obtaining shiny Mew in generation one
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Celebi
Shiny Celebi is only available using the Pokémon Crystal Virtual Console release on the 3DS family of systems. This version of the game gave the player a GS ball upon entering the hall of fame, this item could then be used to encounter a level 30 Celebi with the capability of being shiny, this version of Pokémon Crystal is no longer being sold on the (now discontinued) 3DS Eshop, making this shiny hunt no longer accessible without glitches or external modification of the game.
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Faraway Island Mew
In Japanese Pokémon Emerald, an event item called the "Old Sea Map" was distributed to players between July 17th and August 21st, 2005. If the player was lucky enough to be in Japan at this time they could travel to Faraway Island where they could encounter a Mew. This Mew is the only time players have been able to shiny hunt their own Mew in any Pokémon game, with many players resorting to glitches or external devices to obtain this event.
Click here for more information on the Old Sea Map
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Jirachi
Sometimes considered the hardest shiny to obtain, shiny Jirachi is only obtainable from game specific events with the usual 1/8192 chance of being shiny, either the Pokémon Colosseum bonus disk (with a slightly higher 9/65536 Jirachi's being shiny or a 1/7281 chance of being shiny), or the Pokémon Channel Jirachi (1/8192 odds), both events are only once per save file, meaning resetting your save file (7281/8192 times on average!) or abusing save data corruption are the best options for obtaining this shiny.
A video detailing the save data corruption method
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Deoxys
Also only given out through a limited-time event, Deoxys is much the same as Faraway Island Mew, except it was released wordwide and also available in Pokémon Fire Red and Pokémon Leaf Green. After obtaining the Auroura Ticket players could go to birth island, where Deoxys could beencountered and shiny hunted the same as any other legendary Pokémon
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Shadow Pokémon
Shadow Pokémon are unique to Pokémon Colosseum and Pokémon XD: Gale of Darkness, in Pokémon Colosseum only shadow Pokémon can be Shiny due to the bug allowing this being patched in Pokémon XD. if a shiny is rolled, Pokémon XD will roll again until the Pokémon is not shiny, this was coded incorrectly in Pokémon Colosseum which allows shadow Pokémon to be shiny, shadow Pokémon are the only Pokémon capable of getting the maximum amount of ribbons due to obtaining the "National ribbon" when purified.
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Level 1/100 Magikarp
Starting in generation four, Magikarp became the first pokémon to be obtainable in the wild at level 100, sharing this distinction with Regigigas, unlike Regigigas however, Magikarp (and it's evolution Gyarados) is the only Pokémon obtainable at every level in a single area, with more extreme levels being less common. For levels 1 and 100, only 1% of all Magikarp have a chance of being any level between 1 and 100, this results in a 1/100*1/100 (1/10,000) chance of a Magikarp being either level individually and a 1/100*1/50 (1/5,000) chance of being either level 1 or 100, which still have a 1/8192 chance of being shiny. (1/81,920,000)
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Honey Tree Munchlax
Honey tree Munchlax is a strange case of rarity where most of the difficulty doesn't come from the encounter rates or the Accessibility of the Pokémon, instead this hunt is mostly defined by the effort required to obtain a honey tree Munchlax, only 4 randomly generated honey trees can attract Munchlax, these trees cannot be identified in game until a Munchlax is obtained from one, each tree takes up to 6 hours to generate a Pokémon and Munchlax will only be attracted 1% of the time. After a tree has attracted a Munchlax you can simply reset until the Munchlaxis shiny.
Link to a Munchlax tree finding website
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Pokémon Ranger Manaphy
Easily the most common answer for the rarest shiny Pokémon, the Pokémon Ranger Manaphy egg was intended to be shiny locked, however due to eggs determining their Pokémon ID upon being obtained (not hatched), this egg can be traded to another game for a chance to be shiny, since you have to save before collecting the egg, you cannot re-collect the egg and instead have to trade it to a new game and check it's shininess (for every encounter, at 1/8192 odds!), on top of this collecting more Manaphy eggs is also extremely difficult, as copies of Pokémon Ranger can only provide one egg per cartridge, only after beating the game, this means each egg will require a new copy of Pokémon Ranger and a full playthrough of the game.
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Dragonite
Dragonite is one of the few Pokémon in the series that has a 1% encounter rate, what sets it apart from the others however is that it can only be found in Rippling Water spots, these need to be spawned by walking around, from there Dragonite can only be found by fishing in these spots, both of these requirements decrease the encounter rate and make it much rarer (on top of the fact that it is still a 1/819,200 chance per encounter!)
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Kalos Starters
While generation six did not add many tedious shiny hunts, this generation started a trend on increasing the amount of time that starter pokémon take to recieve, despite the lowered odds the average time for a single encounter has more than doubled, meaning encoutners take much longer than average.
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Salamence
The generation seven games continued the trend started in generation six with shiny Pokémon becoming progressively easier to obtain in subsequent generations however generation seven also allows for a wild level 8 Salamence to be obtained, to obtain this underleveled Salamence you first need to initiate a SOS battle with a wild Bagon, luckily despite being a 1% encounter rate, any Bagon will work meaning that with some time it's not too hard to find. Each Pokémon called in by this Bagon has a 1% chance of being a Salamence, however due to how SOS encounters work, the odds of a shiny Salamence are closer to 1/68,300 due to each individual encounter having a 1/683 chance of being shiny.
Link to more information about SOS battles.
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