Mewtwo is not the only generation one legendary Pokemon that you will have the ability to capture Pokemon X or Pokemon Y. You will have the ability to catch one of the three Legendary Birds seen in Pokemon Red/Blue/Yellow, but unlike those games, you only get one.
The one that you have the ability to catch depends on which starter you chose at the beginning of the game. In my game, I chose Froakie and as a result was able to catch Moltres. If you chose Chespin you will be able to catch Articuno and if you chose Fennekin you will be able to get Zapdos.
Catching one of the Legendary Birds
1. Beat the Elite Four and Pokemon League Champion and play through the end until the game resets and you appear back at your home.
2. There isn’t much you can do besides roam around all of Kalos at this point. Eventually you will come across whichever of the three Legendary Birds that you can catch based on your starter. At this point, that Pokemon will run away before the battle even starts. The only thing you do is throw out your Pokemon to fight and the bird instantly flees. You cannot use Mean Look or anything to prevent this as the battle never happens.
3. Now said Legendary Bird will be located in your Pokedex. Now you can track it just like the three dogs in Pokemon Gold and Silver, and multiple other Pokemon games. Once you find the bird it will flee just as before. I highly recommend buying a bunch of Max Repels and using them once you are in the area where the Pokemon is located. Also make sure to have a Pokemon around level 70 as the first Pokemon in your party if you can. Also, do not use Fly whatever you do as it will move everytime you use it.
4. Now repeat this around 10 times until the Legendary Bird stops moving and is permanently located at the Sea Spirit’s Den.
5. Fly to Coumarine City and take the monorail to the seaside part of the city.
6. Now head west of town to Route 12. Now use Surf in the water and start heading north until you reach Azure Bay. Now head west until you are once again able to surf north. Keep moving north, while moving either east or west to avoid land or a rock formation.
7. Eventually you will reach a cave that is the Sea Spirit’s Den.
8. SAVE RIGHT NOW!
9. Enter the Sea Spirit’s Den and walk forward. Moltres/Articuno/Zapdos will fly down to begin the battle.
The strategy is mostly the same for all three Pokemon. Zapdos can possibly be the hardest to catch due to not being able to paralyze it. For both Moltres and Articuno, bring in a Pokemon that can paralyze with a move like Thunder Wave on turn one. For Moltres this might be more difficult if it gets in Safeguard first. That might be worth a reset if it happens. After paralyzing, then start to attack until you get both down into the red. Zapdos will just start with the second step and you can try to catch it once Zapdos reaches the red or bring in a Pokemon that knows Sleep Powder or any other move that will put it to sleep.
Whichever way you do it on the three, once you have it in the red and with a status effect is possible, start to throw Dusk Balls at the Pokemon as they will give a 3.5x multiplier. Timer Balls will be come even more effective later in the battle as they can get up a 4x multiplier based on the amount of turns in your battle. You could also choose to try a Quick Ball on turn one as well before paralyzing or attacking, but that is up to you. Some have had more success in Pokemon X and Pokemon Y with the Quick Ball than in the past, so it’s not a bad idea to try if you have one. Just remember that the 4x multiplier only occurs on the first turn.
When all is said and done, you will have one of the Legendary Birds on your team now!