I'm just going to list most possible ways to get Mythicals excluding limited distributions. Also, before you start reading... here's all the that can't be obtained with these methods: Meloetta, Genesect, Diancie, Hoopa, Volcanion, Zeraora, Zarude, and Dada Zarude.
Generation 2
Crystal
GS Ball (Celebi)
● Allows the player to battle a Celebi at the shrine in Ilex Forest.
Generation 3
Ruby/Sapphire
Eon Ticket (Latias/Latios)
● Allows the player to go to Southern Island, where they can find a Latias (Ruby)/Latios (Sapphire).
Emerald
Eon Ticket (Latias & Latios)
● Allows the player to go to Southern Island, where they can find a eon duo member not roaming around Hoenn.
AuroraTicket (Deoxys)
● Allows the player to go to Birth Island, where they can find a Deoxys.
MysticTicket (Ho-Oh & Lugia)
● Allows the player to go to Navel Rock, where they can find a Lugia and Ho-Oh.
Old Sea Map (Mew)
● Allows the player to go to Faraway Island, where they can find a Mew.
Fire Red/Leaf Green
AuroraTicket (Deoxys)
● Allows the player to go to Birth Island, where they can find a Deoxys.
MysticTicket (Ho-Oh & Lugia)
● Allows the player to go to Navel Rock, where they can find a Lugia and Ho-Oh.
Generation 4
Diamond/Pearl/Platinum
Azure Flute (Arceus)
● Allows the player to go to the Hall of Origin, where they can find an Arceus. (unreleased)
Member Card (Darkrai)
● Allows the player to go to Newmoon Island via the Harbor Inn, where they can find a Darkrai. (unreleased)
Oak's Letter (Shaymin)
● Allows the player to go to Flower Paradise via Seabreak Path, where they can find a Shaymin. (unreleased)
Secret Key (Rotom)
● Allows the player to go enter Rotom's Room in the Team Galactic Eterna Building, allowing them to change the form of Rotom. [Platinum] (I'm assuming)(not mythical, just worth mentioning imo)
Heart Gold/Soul Silver
Enigma Stone (Latias/Latios)
● Turns into a Soul Dew and allows the player to battle a Latias (Soul Silver) or Latios (Heart Gold) in front of the Pewter Museum of Science.
Generation 5
Black/White
Liberty Ticket (Victini)
● Allows the player to go to Liberty Garden, where they can find a Victini
Generation 6
Omega Ruby/Alpha Sapphire
Eon Ticket (Latias/Latios)
● Allows the player to go to Southern Island, where they can find a Latias (Omega Ruby)/Latios (Alpha Sapphire).
Generation 7
Sun/Moon/Ultra Sun/Ultra Moon
(Megearna)
● A Magearna QR Code event was specially distributed for Sun, Moon, Ultra Sun, and Ultra Moon. Unlike most other QR Codes, it unlocks an event in the player's game, and each of the QR Codes below only works for games from a specific region. These codes cannot be scanned until the player becomes Champion after beating the Alola League.
(Partner Cap Pikachu)
● In Pokémon Ultra Sun and Ultra Moon, another QR Code for a Partner Cap Pikachu was added to the game. Like Magearna, these codes are region-specific, with the exception of the American and PAL region sharing the same code. They cannot be used until the player reaches Akala Island. [USUM]
Generation 8
Sword/Shield
(Keldeo)
● After capturing Cobalion, Terrakion, and Virizion, a pair of brown footprints will appear near a pot on an island in Ballimere Lake. After interacting with the footprints and making a curry with Cobalion, Terrakion, and Virizon in the party, Keldeo will appear on the island.
Brilliant Diamond/Shining Pearl
Azure Flute (Arceus)
● Allows the player to go to the Hall of Origin, where they can find an Arceus.
Member Card (Darkrai)
● Allows the player to go to Newmoon Island via the Harbor Inn, where they can find a Darkrai.
Oak's Letter (Shaymin)
● Allows the player to go to Flower Paradise via Seabreak Path, where they can find a Shaymin.
(Mew & Jirachi)
● If the Nintendo Switch system being used has save data from previous mainline Pokémon games, the player may talk to an appropriate NPC (Gentleman/Madame) in Floaroma Town to receive these Mythical Pokémon. Players of Let's Go, Pikachu!/Let's Go, Eevee! can receive a Mew, while players of Sword/Shield can receive a Jirachi. These Mythical Pokémon cannot be Shiny.
Legends: Arceus
(Phione)
● In the mission "The Sea's Legend", you can catch (static encounter) Phione. It also has a 1.94% chance of spawning normally.
(Manaphy)
● In the same mission, 1 Manaphy is available to catch per game (static).
(Cresselia)
● Cresselia is found as part of the "The Plate of the Moonbreak Arena" mission after completion of the main story. In this story you have to go to Moonbreak Arena where Melli will ask your help to get rid of a Pokémon that has displaced Electrode. Go into the arena and you'll find Cresselia waiting for you.
(Darkrai)
● As part of the " The Darksome Nightmare" Request if you have a Pokémon Brilliant Diamond or Shining Pearl savefile, when given this request at Laventon's Lab, Cael will appear and tell you of strange goings on in the Clamberclaw Cliffs. Go there at night and Darkrai will surprise you and challenge you to a battle.
(Shaymin)
● As part of the "A Token of Gratitude" Request if you have a Pokémon Sword or Shield savefile, when you get to the camp, Medi will give you a Gracidea and say how she wants to give gratitude to the Pokémon she found there and say she can't remember where the flowers are. They are in the Floaro Gardens in the north west but when you get there, the flowers have died. Medi will appear and will call out to Shaymin so she calls out to say thank you which revitalises the flowers and Shaymin comes to battle.
(Arceus)
● After defeating Giratina at the Temple of Sinnoh, your Celestica Flute turns into the Azure Flute and you can play it to summon Arceus. However, unless you have caught every other Pokémon in the region, you cannot continue on.
Return with your Pokédex complete (except for Phione, Manaphy, Darkrai, Shaymin and Arceus), and you will be able to challenge Arceus. You will get taken up to the Hall of Origin for one final frenzied battle.
You will get given Mysterious Balm, converted from your Arc Phone, and you will need to throw it at Arceus to get to the battle. After you have defeated it, you will be given a piece of Arceus and its Legend Plate.
Spin-offs
Pokémon Ranger
(Manaphy)
● There are no items but, there is a code for a Manaphy egg and it still works: P8M2-9D6F-43H7
The Manaphy can be transfered to the main series games.
Note: Password menu is opened with R + X + Left
No longer possible as of January 31st, 2019 (I'm assuming)
My Pokémon Ranch
● Here are steps to get Mew:
1. (if you don't already have it) Download My Pokemon Ranch
2. Open My Pokemon Ranch
3. Press 'Connect to DS' on ranch HUD
4. Turn on either Pokemon Diamond or Pokemon Pearl
5 On the DS, press "Connect to Wii"
6. Press 'Deposit All' to deposit all Pokemon from one box faster
7. Deposit all Pokemon you have collected until you reach 1000 Pokemon
8. Collect a Mew from Hayley in return for any random egg
Pokémon GO
(Meltan)
● Meltan can be obtained with special missions subtitled "Let's GO, Meltan". In order to catch Meltan, it is essential to have a Mystery Box, which can be received by sending Pokémon from Pokémon GO to Pokémon: Let's Go, Pikachu! or Pokémon: Let's Go, Eevee!.
Sources
Source (Mew)
Source (Manaphy Egg)
Source (event items)
Source (QR codes)
Source (Meltan)
Source (Mew & Jirachi)
