The single strongest Pokémon in Pokémon: Let’s Go, Pikachu! and Let’s Go, Eevee! is the Psychic-type Mewtwo. It is so powerful, in fact, that the game won’t even allow you to attempt to catch it until you’ve become the Champion of the Kanto region. Once you’ve defeated the Elite Four and secured your title as Champion, a new area of the game opens up to you, which is where Mewtwo is hiding.
This new area is Cerulean Cave, which you can get to by crossing the bridge to the north of Cerulean City, then using Sea Skim on the strip of water just to the left of the bridge and surfing down until you come across the opening to a cave with a Coach Trainer outside of it. Inside Cerulean Cave, there are plenty of strong wild Pokémon you may want to catch on your way to Mewtwo. On this first floor, there are several ladders leading up to the second floor. Take any of them; they all lead to the same place. The second floor is one, big, wide-open area with a lot of ladders leading back down to the first floor. You’ll want to take the ladder in the top left corner of this area, which will lead you back down to the first floor, but into an area you couldn’t reach on the first floor previously. This new section of the first floor will have yet another ladder leading down, this time to the cave’s underground floor. Take this ladder and arrive on the cave’s bottom floor. From here, the path is pretty straightforward and will take you right to Mewtwo.
You should probably save the game before interacting with Mewtwo, just in case. When you’re ready, interact with Mewtwo by going up to it and pressing the A button. There will be a short cutscene before you’re thrust into battle with the legendary creature. You’ll need to defeat Mewtwo in battle before being given a chance to catch it. Mewtwo is on Level 70, making it by far the strongest wild Pokémon in the game, so be prepared. As a Psychic-type, Mewtwo is weak to Ghost, Bug, and Dark moves, so keep that in mind. Once you’ve defeated Mewtwo in battle, you’ll have to catch it like any other wild Pokémon. If you still have your Master Ball, now would probably be a good time to use it. Otherwise, you’ll want to come prepared with tons of Ultra Balls.