Like all the other main Pokémon Game lines, Pokémon Sword and Pokémon Shield feature Legendary Pokémon that the player can capture. If you own Sword, you can get Zacian. If you play Shield Zamazenta is the Legendary Pokémon that you can capture.
The new generation of Pokémon games mix up the formula a bit this time around. In the past, you've always been able to receive at least one Legendary Pokémon before taking on Elite Four and attempting to become a Pokémon Champion. This time, however, you won't be able to get it until the Championship game.
In Sword and Shield, your last match to become champion of the Galar region is against Lee. Once you defeat it, the credits will be cast, but don't worry; the game is not yet completely finished!
Once you have watched the credits and resumed the game, you will be back at your home, where the game originated. Professor Magnolia will come to your house and give you a Master Ball for helping to save Galar. This ball never misses no matter what Pokémon it is thrown at, so save it!
Go to the Sleeping Weald, where you obtained the Sword and Shield that summons Zacian and Zamazenta. Hop will be there and challenge you.
After the battle, you will be challenged by two brothers who claim to be of the royal line. Defeat them to collect the sword or shield. Hops will lose to each other, and your mission going forward will be to hunt them down while battling The Energized Pokémon in almost every Gym that participated in the challenge.
You'll know you're near the end when you face off against one The Brothers in the basement of Hammerlocke Stadium. This is the same area where you fought President Rose.
After defeating him, you'll take the elevator to the roof, where you'll face off against any Pokemon that isn't on your blanket. If you're playing Shield, it'll be Zacian. If you are playing Sword, you will face Zamazenta.
During this fight, you cannot catch the legendary. Do not even try. You must defeat him in battle, which will appeal to the legendary other. Close this fight, the Pokémon on the cover of your game will be catchable. Use your Master Ball and you will catch Zacian or Zamazenta.
Return to the Sleeping Weald, where Hop will console the legendary Pokémon you defeated in battle. He'll then grab the Legendary himself and challenge you to one final battle. This is the last battle before the game ends, so be prepared for a tough fight.