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By getting a hold of the Eon Ticket, and after your first trip to Southern Island during the main game, where you get both the Mega Bracelet and one of the Eon Pokémon (LatiosOR/LatiasAS), you can use the Eon Ticket to return to Southern Island and collect the other Eon Pokémon, LatiasOR/LatiosAS.
Getting the Eon Ticket
After the original distribution from digital codes, depending on your region, for the Mystery Gift, it is possible for players through the Nintendo Network or Local Wireless to pass on the Eon Ticket to each other as long as the StreetPass feature on their Nintendo 3DS/2DS system is activated and enabled for Pokémon Omega Ruby and Alpha Sapphire. By using the BuzzNav feature in your PokéNav Plus it can identify that you received the Eon Ticket for your game and then you head to a Pokémon Center. There talk to the special representative to receive the ticket. After this it is also possible to distribute it to other players using this method.
Using the Eon Ticket
Return to Southern Island
At any time after you have visited Southern Island during the main story, head to Petalburg Gym and talk to Norman. He'll notice that you have the Eon Ticket, which he hasn't seen for 11 years, and reveals it is given to those who have earned the ability to wield Mega Evolution. Recognizing your Mega Bracelet, Norman will take you to the harbor in Slateport City and a sailor will take you to Southern Island. If you need to go back to prepare your team, talk to the Sailor and you can return to Petalburg Gym and start this event again.
Catching the remaining Eon Pokémon
Head back to the enclosure where you originally met LatiosOR/LatiasAS and LatiasOR/LatiosAS will be there. Unlike their counterparts they won't agree to join you and instead will challenge you to a battle. They are at level 30, the same as their counterparts when they joined your team in the main story.
Depending on where you are in the game and the levels of your team, there will be varying strategies in how to catch Latias/Latios. If your team is of similar level the standard wearing it down and paralyzing/putting it to sleep should work fine. If your team is higher levelled to where one attacking move could faint it, use a preset damage move like Dragon Rage or use False Swipe to get their HP down low enough to increase the catch chance, in addition to afflicting a status condition. Steel-type Pokémon can be useful for being able to withstand their Psychic and Dragon-type moves. Also Electric-type type Pokémon can come in handy here as Psycho Shift will fail to pass a paralyzed status onto said Pokémon. Because it is Dual Electric/Steel type, Magneton or Magnezone are well suited for withstanding their attacks and using Thunder Wave to paralyze them. When ready use Ultra Balls or Timer Balls (once enough turns have passed) to try to catch it.
If you accidentally knock out Latias/Latios, their health resets to maximum as if nothing happened, and therefore will give you infinite attempts at capturing them. While you can instantly re-challenge them, if your team is too weak from the previous fight, then it would be best to return to Petalburg City first to have them healed.
Once you have successfully caught Latias/Latios you will find an item on the ground, the Soul Dew, which when held by either of the Eon Duo can enhance their Special Attack and Special Defense by 50%. After this head back to the entrance and talk to the Sailor to return to Petalburg City to end the event.