After you have got the national dex, go to pal park and talk to Professer Oak. He should in there. Afterwards, he will leave. Now head to Eterna City and approach the house across the street from the Gym. Enter the house and talk to professer Oak again. He will say that the legendary birds are in Sinnoh. If you look at your marking map application, you'll see the roaming pokemon. Chase them and they will battle you. Save the game. Make sure you use mean look as your first move and ,by the way, your pokemon's speed must be faster than theirs. They know roost so after using mean look try a move such as heal block. Once you get their HP to very low, throw an ultra ball (if daytime) or dusk ball (night time). If it faints quit without saving the game so you can try again. Good luck dude!
