What legendary shiny pokemon are legitimately obtainable as of Sword/Shield?

Some Legendary and Mythical Pokemon cannot be shiny. As of the release of generation 8, these are: Victini, Keldeo, Meloetta, Hoopa, Volcanion, Cosmog and Cosmoem, Magearna, Zeraroa, Zacian, Zamazenta and Eternatus.

These Pokemon cannot be legally shiny under any circumstance. That aside, the following Pokemon are also "Shiny Locked". This means that when they are encountered in-game in these generations, they are hardcoded to never be shiny. They can however still be shiny through events or encounters from other games.

Event Pokemon have their shiny status predetermined if received through Mystery Gift. For Pokemon that have in-game events associated with them, reference the list below.

Generation 5

• Victini
• Zekrom
• Reshiram

Generation 6

• Articuno
• Zapdos
• Moltres
• Xerneas
• Yveltal
• Zygarde
• Kyogre
• Groudon
• Deoxys

Generation 7

• Tapu Koko
• Tapu Lele
• Tapu Bulu
• Tapu Fini
• Cosmog
• Solgaleo
• Lunala
• Nihilego (Only in Sun and Moon, not locked in Ultra Sun and Ultra Moon)
• Buzzwole (Only in Sun and Moon, not locked in Ultra Sun and Ultra Moon)
• Pheromosa (Only in Sun and Moon, not locked in Ultra Sun and Ultra Moon)
• Xurkitree (Only in Sun and Moon, not locked in Ultra Sun and Ultra Moon)
• Kartana (Only in Sun and Moon, not locked in Ultra Sun and Ultra Moon)
• Guzzlord (Only in Sun and Moon, not locked in Ultra Sun and Ultra Moon)
• Necrozma

Generation 8

• Starters (gift only, can still be bred as shiny)
• Charmander (gift only, can be encountered as shiny or bred)
• Gigantamax Pikachu (gift only, can be encountered as shiny)
• Gigantamax Eevee (gift only, can be encountered as shiny)
• Toxel (gift only, can be encountered as shiny or bred)
• Zacian
• Zamazenta
• Eternatus

Let's Go Pikachu and Eevee

• Partner Pokemon

Source