Galar introduced battle-condition evolutions. Sirfetch'd evolves after landing three critical hits in one battle. Runerigus evolves by taking damage under a specific stone arch. Galarian forms created new evolution paths, and Alcremie uses sweet items with specific spinning patterns for 63 forms.
Land three critical hits in a single battle. That's it, but it's trickier than it sounds. Give Galarian Farfetch'd its signature Leek item (50% chance it holds one when caught) and use Focus Energy. With both active, you hit 100% crit rate. Fight a tanky wild Pokemon so you have enough turns to land all three. Farfetch'd is Sword-exclusive, so Shield players need to trade for one.
Galarian Yamask needs to take at least 49 HP of damage in one battle without fainting, then you walk under the stone arch in the Dusty Bowl area of the Wild Area. The game doesn't tell you any of this. If Yamask faints before you reach the arch, the damage counter resets and you start over.
63 total. Milcery evolves into Alcremie by holding a Sweet item and spinning your character. The form depends on which Sweet you use (7 types), which direction you spin, how long you spin, and whether it's during the day or night. It's the most complex cosmetic evolution in the entire series.
Several. Galarian Zigzagoon becomes Linoone, then Obstagoon (first three-stage Galarian chain). Galarian Mr. Mime evolves into Mr. Rime. Galarian Corsola becomes Cursola. Galarian Slowpoke evolves differently depending on whether you use a DLC item from Isle of Armor or Crown Tundra. And Galarian Ponyta becomes Rapidash with a type swap to Psychic.
Not through normal gameplay. Sword and Shield still uses the traditional trade mechanic for Gengar, Machamp, Conkeldurr, and the rest. The Linking Cord item that removes this requirement wasn't introduced until Legends Arceus. You need a trade partner or a second Switch.
Isle of Armor brought the Galarica Cuff (Galarian Slowpoke to Slowbro) and Galarica Wreath (to Slowking). Crown Tundra added Reins of Unity for fusing Calyrex with its steed. Both DLCs also added evolution stones in new locations and Max Raid dens, making it easier to stock up on stones you couldn't farm easily in the base game.