If you are looking to complete your Pokédex in Pokémon Sword and Shield, you must spend some time exploring the Galar region. Fortunately, you can find the majority of The Pokémon in the Wilderness Area, just outside of Motostoke and Hammerlocke. Embrylex is a particularly difficult Pokémon to locate, which you need to become a Tyranitar. It does, however, have a defined spawn location.
You can find this Pokémon in the Wild Area and you will have access to it when you receive the Motisma Bicycle Upgrade. When you have that, head to the wilderness area just outside of Hammerlocke and head west to Outrage Lake. You can find Embrylex on the other side.
Unfortunately, you won't see them in the outside world. It only appears as The exclamation marks in the grass. So you have to explore the wild area thoroughly to have a decent chance of locating one. You only have a five percent chance of finding it too. You need to make sure that the weather conditions are cloudy or sunny.
If you want a little luck, you can find Embrylex's evolved form, Ymphect, in the same sector, and she has the chance to spawn in the onworld. Relying on finding a Ymphect before finding an Embrylex is not the best approach as you are more likely to locate the first evolution. You can find a Ymphect during a sandstorm so that it spawns in different weather conditions.
When you discover your Embrylex or Ymphect, be careful not to use a Grass or Water type, as you don't want to make it pass out when you tap it. They are both land and rock type Pokémon.
An Embrylex evolves into Ymphect at level 30, then it becomes a Tyranitar at level 55, which is a Rock and Dark-type Pokémon.