I have found out the secret to get every legendary in the Pokédex, well, almost every legendary. I became a Tepig breeder and put one up for trade for an Espeon and it came in like 2 minutes. I found out Tepig was a rare Pokémon or something and I got every Pokémon I asked for but when I ask for Deoxys or Shaymin I get nothing.
What's up with that?
This is because Deoxys and Shaymin are mythical Pokemon.
These Pokemon cannot be traded on the GTS as they are too rare and you can only get them through events.
Here's a list of Mythical Pokemon: