Okay, I just got through with Team Flare, and getting the rare pokemon in their lab. Man that seemed like that took forever.
The first time around, I damaged it as usual, and threw an ultra ball at it. It actually worked.... But then things didn't run so smoothly after that. Put it into battle, and got defeated by the boss with it after I defeated 1 or 2 of his pokemon down.
I restarted the game, to see what would happen if things were differently. I damaged it all the way through one time to see what would happen. It's interesting that the game forces you to catch it.
I tried ultra ball again, unsuccessful. Tried pokeball just to amuse me, didn't work of course. My last attempt was damaging it, and threw a Luxery ball at it. Finally caught it again.
Last after fighting the boss again, no sweat until he got to his Gyrados and mega evolved it. Tried using my Pikachu for the super effectiveness, but no go. I ended up using one of my other pokemon, and finally defeated him.
So in another universe that never was, I caught it with an Ultra ball. But now, instead ended up catching it with Luxery ball instead. Go figure.
I had a Master Ball, but I'm actually saving that one for later.