Firstly, I would recommend you do either:
a) Get another game
b) Reset your current game.
This is so you can trade your precious EV trained Pokemon. If you use Bank, many transferring a good amount of your Pokemon to their would be a good idea. This is because these legendaries you have caught will never be able to catch again.
TIPS AND TRICKS
Final Gambit: Confused? Final Gambit does damage based on your current HP, and makes you faint in said process. If you look on an online calculator, it is very easy to compare the legendaries highest HP (with 31 IVs) and the HP of your Final Gambit user. For example Kyogre has a max HP of 175. If we have a Final Gambit user with a HP of 174, it will either faint the legendary or bring it down to 1HP. If it lives on 1 HP, you have a 31 IV Legendary!
Synchronise: If any Pokémon with Synchronise is at the front of your party, they have a 50% of having that Pokemon's nature. Very helpful for getting the right nature.
Abilities such as Intimidate: Abilities that have an actual effect are very helpful. For example, we want a Kyogre with max speed potential. We look at Kyogres max speed (121 with Timid) and we send out a Pokémon with a speed stat of 120 with Intimidate. If the Kyogre has max speed, it's Ability Primordial Sea will occur before Intimidate, in any other case your Intimidate user will out speed.
