(Please note that the recommendations below are largely made for in-game play. A Hawlucha in a competitive environment will likely make use of different moves to accommodate for smarter, more adaptive opponents. If you've got an alternate Hawlucha moveset you'd like to share, please attach it in the comments.)
A luchador and a bird mixed into a single pokémon? Ah, you crazy Nintendo designers, you. Hawlucha is a fun pokémon to use in a battle, and though it's not necessarily the best thing to come out of the latest generation of games it still has a lot to offer to a team facing slower opponents.
Type: Fighting / Flying
Hawlucha is a single-form pokémon. It doesn't currently evolve from, or into, any other pokémon.
Bug, Dark, Fighting, Grass. Immune to Ground.
Electric, Fairy, Flying, Ice, Psychic.
Fighting-types have a tendency to fall into one extreme or another: either very defensive or very offensive. Hawlucha is a little more balanced in this respect, which isn't necessarily a good thing, though it still has the makings of a good sweeper with a beefy Speed stat and a good Attack. Everything else is merely average, save perhaps Special Defense which falls a little below the bar. This last fact can be a bit problematic, as Hawlucha isn't that difficult to swat in one hit.
Unburden: If the pokémon uses or loses its hold item during a battle, its Speed is doubled while it's still in play. Hawlucha's already rather quick; Unburden will allow it to outspeed virtually anything. Though I like Unburden in theory, it forces you to hope that the enemy will use an attack targeting whatever berry you have equipped. If you do decide to use an Unburden Hawlucha, I'd suggest giving it something to restore its HP.
Limber: This pokémon is immune to paralysis. In theory Unburden is the better ability, but I find Limber more useful because human opponents a) love Thunder Wave and b) tend to forget that Hawlucha has Limber.
Mold Breaker: Moves will work regardless of abilities that say otherwise. For example, a Hawlucha that uses Dig will hit a pokémon that has Levitate. This could be useful, but Hawlucha doesn't have a ton of moves which merit its inclusion. This is a hidden ability.
No two bones about it, Hawlucha is a sweeper. It's meant to wipe out enemy teams. Its primary weapon is High Jump Kick, which, though potentially risky, will tear apart pokémon even with high Defense scores. Sky Attack or Fly are solid choices for flying-type STAB moves; I prefer Fly, as it takes Hawlucha out of harm's way for a turn rather than leaving it open to attack. Acrobatics is a possibility as well, though for it to be truly effective Hawlucha won't be able to carry an item. (Possibly fun for an Unburden Hawlucha? Think about it.)
Beyond that you can toss in another attacking move - X-Scissor and Poison Jab are fine candidates - and a support move, either Swords Dance or Hone Claws. I prefer Hone Claws for the small bump in Defense, something Hawlucha often needs, but it's up to you.
EV / Super Training
Hawlucha isn't that great at anything other than attacking, so it needs to ensure that it can land a hit before its opponent can move. Consequently, Speed is your number one priority. Couple that with the rest of your EVs going into Attack and you've got quite a powerhouse hitter. It won't be able to take much damage, but it shouldn't be getting hit in the first place. Hawlucha's other stats are fairly negligible as far as EV training goes - if you're going to stick those points anywhere, put them in Special Defense. A physical hit to a Hawlucha will probably be a flying-type move, whereas a special attack targeting its weaknesses could be any number of things.
Catching a Hawlucha
There's only one place to catch Hawlucha in Pokémon X and Y (besides the Friend Safari, of course), and that's Route 10. Search the menhir fields and you should find a Hawlucha in fairly short order.