If Pokémon was real, how hard do you think it would be to defeat/catch a Legendary/Mythical?

Maybe with a Master Ball but even then there have been cases in the anime where it fails, I remember Whiscash eating a Master Ball.

Um.
I think he meant assuming we have Pokemon equipment too.
Also, I believe to remember what separated a Pokemon from an animal was their ability to become a form of energy that would go into Poke Balls. Also, Pokemon (at least some) like to battle, so capturing them and having them battle seems fine to me… IF they want to.

If there were only one of something, or even a very small population of them, throughout the world that everyone wanted, they would be captured the second they were discovered.

That is assuming that the relevant government bodies in the region did not try to capture it for themselves, put in sanctions and regulations to protect it and guard it, or try and eliminate it for the danger it posed.

In the pre-internet era, your average citizen would never know a legendary Pokémon existed until days or weeks after its discovery and capture, assuming whoever discovered and captured it felt compelled to advertise that fact and had the means to do so.

In the internet age, the first you would hear about it would be the person who caught it bragging in a livestream that they had caught it.

Again, assuming the powers that be did not crack down immediately. In a world with real Pokémon, even the capture and training of regular Pokémon would be more heavily regulated than animals and guns combined.

No government is letting a ten year old run around with Team Rocket's genetic experiments, or (possibly literal) gods.

Pokemon never quite works in the real world.

Except wait- in the Pokemon games, mainly in Legends Arceus, we got to learn that people have been trying to tame Pokemon since old times- and they did it!
So by modern times they would probably be accepted as normal. Chances are, we would have built our civilization around these things! Pokemon battle would likely be a massively popular sport. Instead of going to watch the Super Bowl, you'd be watching the Pokémon League or something. A Pikachu power plant is mentioned in dex entries. Also, in the games, it seems like not that many people really can call themselves 'Pokemon Trainers'. They might have Pokemon, and they might occasionally have a battle, but that's like 'owning a dog and playing with it' common!
The Legendary Pokémon… I bet that some places would be like Alola, and respect them greatly. Others would be like Galar and remember them only from legends. Some would be researching them, whether to try to make a breakthrough or do something truly terrible. But I bet they would stay the way they were in the games without the player-
Almost all uncaptured.