Not all Pokémon are mythical, in the same way how not all Pokemon are cute. Here is a list of Pokémon who have a Mythical classification according to Bulbapedia. It includes some legendaries with legendary runes (or TMs) like Latias and Zeraora, which may also be eligible for the title of “mythical” as well.
- Mew : Mew is blocked from being obtained in any game or direct way, but can still be seen on most games through glitches and hacking. A video of gameplay footage can be found here [link]. After the release of Pokemon Crystal and movies 4-5 respectively for Red/Blue/Yellow where Mew starred as the main character in each film, Nintendo decided to boost Mew’s status as a legendary.
- Celebi : Celebi is only available in the Japanese Gold and Silver via a direct giveaway from their own event. Celebi was a post-game gift for X/Y and ORAS, but can be obtained by normal means through an in-game trade in Black/White 2 and Zeraora trophies have been released for Ultra Sun/Ultra Moon’s launch which include a code that has a chance of being an actual Celebi.
- Jirachi : Jirachi is only available through a direct event giveaway from Nintendo by playing the Japan-exclusive mobile game “Pokemon Wishing Star/Star of Wish”. In Pokémon Colosseum and X/Y, Jirachi can be accessed as an in-game trade. In ORAS, it’s distributed by Nintendo through an in-game event. Wishing Star is not compatible with US/EU region phones, but it can be played on PC
- Manaphy : Manaphy can only be obtained by participating in the direct event giveaways from their own events. Players who want to get Manaphy need to download “Pokemon Ranger: Guardian Signs” and use the special Manaphy quest which is only available for a limited time upon completing the story of “Guardian Signs.”.
- Shaymin : Shaymin’s distribution method is similar to Jirachi. It can be obtained by participating in Nintendo’s event giveaways or through distributions at theaters and retail stores under the title “Shaymin Gifts.” In Pokémon Omega Ruby/Alpha Sapphire, it can be accessed as an in-game trade. Shaymin was distributed in-game in US/UM through a QR code by which you can find your own Shaymin. .