pokemon-sword-shield
Are there any Pokemon not available to catch in sword and shield that would make it impossible to complete the Pokedex without involving another Pokemon game?
If so, what other Pokemon games are required and what is the method for attaining these Pokemon?
Isle of Armor
In the Isle of Armor DLC, there is a mini-game in which you are tasked find Alolan Digletts throughout the island. By collecting these Diglett, you will be given various Alolan forms (as well as a Kantonian form and Alola starter) as rewards for returning them to their owner.
Base Version
You cannot obtain Alolan forms in the base version of Sword and Shield, but you can by transferring Pokemon into the game via Pokémon Home (as long as the base form exists with in the Pokedex) or by trading with others players who transferred them from Pokemon Home
Alolan forms do existin the Galar region, as Alolan Meowth can be found in one of the camps. This camp is located on Route 7, and is known as “Renee’s Camp”
There are plenty of trades to perform in Sword/Shield! Here's the ones I've been able to find, as well as some from other sources
These trades are available in both games:
Bunnelby → Skwovet ♂ (Motostoke Pokemon Center)
Nickname: Cheekers, Level: 10, Nature: Mild, Ability: Cheek Pouch, Held Item: Oran Berry, Dynamax: 1
Meowth (Galar) → Meowth (Kanto) ♂ (Turrfield Gym)
Nickname: Cash, Level: 18, Nature: Timid, Ability: Technician, Held Item: Sitrus Berry, Dynamax: 1
Minccino → Cottonee ♀ (Hulbury Market)
Nickname: Candyfloss, Level: 23, Nature: Modest, Ability: Prankster, Held Item: None, Dynamax: 1
Toxel → Togepi ♀ (Hammerlocke - Outside Vault)
Nickname: Snips, Level: 25, Nature: Timid, Ability: Serene Grace, Held Item: None, Dynamax: 1
Yamask (Galar) → Yamask (Unova) ♂ (Ballonlea Gym)
Nickname: Masky, Level: 36, Nature: Bold, Ability: Mummy, Held Item: None, Dynamax: 2
Obstagoon → Mr. Mime (Kanto) ♂ (Spikemuth - Near battle area)
Nickname: Mymo, Level: 40, Nature: Calm, Ability: Soundproof, Held Item: None, Dynamax: 1
Frosmoth → Duraludon ♂ (Wyndon - 4th house down from the stadium)
Nickname: Linear, Level: 50, Nature: Adamant, Ability: Heavy Metal, Held Item: None, Dynamax: 3
These trades are exclusive to either Sword or Shield as noted below:
(Sword) Maractus → Hatenna ♀ (Stow-on-Side - Top of leftmost building)
Nickname: Fringe, Level: 30, Nature: Quiet, Ability: Anticipation, Held Item: None, Dynamax: 1
(Shield) Maractus → Impidimp ♂ (Stow-on-Side - Top of leftmost building)
Nickname: Peepers, Level: 30, Nature: Random, Ability: Anticipation, Held Item: None, Dynamax: 1
(Sword) Vanillish → Throh ♂ (Circhester - Ice cream stall)
Nickname: Reddos, Level: 37, Nature: Adamant, Ability: Inner Focus, Held Item: None, Dynamax: 2
(Shield) Vanillish → Sawk ♂ (Circhester - Ice cream stall)
Nickname: Bluebop, Level: 37, Nature: Adamant, Ability: Inner Focus, Held Item: None, Dynamax: 2
Sources for the ones I was unable to find originally:
Best Answer
Depends on what you mean by 'Complete the Pokedex'.
Sword and Shield's Pokedex does not feature all Pokemon. That is to say: about 400 Pokemon were left out of the game code, they don't exist in Sword/Shield or the Galar region in which they're based.
Completing the Pokedex
It is possible to complete the Galarian Pokedex (i.e. catching and trading between Sword and Shield), but not the full, 'National' Pokedex. In fact, the concept of a 'National' dex was removed from the game entirely. Here's a relevant quote from an interview with Junichi Masuda, the main developer behind the Pokemon series:
Regarding Transfer of Old Pokemon
There is currently no way to transfer Pokemon up from previous generation games (and although that will change with the arrival of 'Pokemon Home', 'cut' Pokemon will not be able to be transferred into Sword/Shield).
Masuda continues with regards to the transfer mechanism (emphasis mine):
If you're interested, here's an image representation of all the Pokemon that were cut from the Galarian Pokedex (hidden behind spoiler markdown, click or mouseover to view):
Image sourced from r/Pokemon