HELP. IN NEED OF HELP.

[Starkler]

So I just joined today, got 5 level 100s, and I was just wondering how I can get good pokemons? I only got a starter pokemon and 4 other pokemon from a map.
What I'm asking is how do I get a Lugia and such? I highly doubt people would trade a level 100 non elite for a level 5 Lugia Elite.
So how can I earn elite pokemon?

[E 3k]

Legendaries(Lugia, etc.) can be caught after you beat every Gym Leader, other than the Frontier Brains. That is 49 badges. If you beat all 56 Gyms and heal 10 pokemon at the center, you can also go to the secret map to catch fusion pokemon(Two pokemon in one)

[Zizo123]

Legendaries(Lugia, etc.) can be caught after you beat every Gym Leader, other than the Frontier Brains. That is 49 badges. If you beat all 56 Gyms and heal 10 pokemon at the center, you can also go to the secret map to catch fusion pokemon(Two pokemon in one)

Also you can get a species of pokemon called plasma pokemon once you have all 56 badges.