Like all other mainline Pokémon Game, 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 Pokemon that you can capture.
The Next Generation of Pokemon games are mixing up the formula a bit this time around. In the past, you've always been able to receive at least one legendary Pokemon before taking on the Elite Four and attempting to become a Pokemon champion. This time, however, you won't be able to get it until the championship game.
In Sword and Shield, your final match to become champion of the Galar region is against Lee. Once you defeat him, the credits will roll, but don't worry; the game is not completely over yet!
Once you've watched the credits and resumed the game, you'll be back at your home, where the game originated. Professor Magnolia will come to your home and give you a Master Ball for helping save Galar. This ball never misses no matter what Pokemon it's thrown at, so save it!
Go to the Sleeping Weald, where you got 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 royal lineage. Defeat them to collect the sword or shield. The hops will lose to each other, and your mission moving forward will be to track them down while battling The Boosted Pokémon at nearly every Gym that has participated in the challenge.
You'll know you're near the end when you face off against one of The Brothers in the basement of Hammerlocke Stadium. This is the same area where you fought President Rose.
After beating it, you'll take the elevator to the roof, where you'll battle any Pokémon that aren't on your cover. If you play Shield, it will be Zacian. If you play Sword, you will face Zamazenta.
During this fight, you cannot catch the legendary. Do not even try. You must defeat it in combat, which will call upon the other legendary. Close this fight, the Pokémon on the cover of your game will be catchable. Use your Master Ball and you'll catch Zacian or Zamazenta.
Return to the Slumbering Weald, where Hop will console the legendary Pokemon you defeated in battle. He will then grab the Legendary himself and challenge you to one last battle. This is the last battle before the end of the game, so be prepared for a tough fight.