You need to overcome the weaknesses:
1. Gardevoir can't do anything for one turn after using the beam. You can't even switch.
2. Fairy-powered beam won't kill anything steel, fairy, or fire or poison type. Furthermore, it won't kill anything with good special defense. After all, it's actually not THAT impressive. A single nasty plot + STAB move is way more powerful than that pixellate hyper beam. So guys like Snorlax or Florges would just laugh at your face.
3. Mega Gardevoir won't have any items. This means no leftovers... no lum berry... no sitrus berry... no choice specs... etc.
4. Mega Gardevoir is quite slow for a sweeper. 100 speed won't win any awards. It's also quite squishy and will die easily to things like Talonflame's brave bird, Azumaril's aqua jet, or Scizor's bullet punch. Even a poison jab from something like Gliscor would obliterate it in one hit.
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So basically you need other mons to clear out the enemy mons that can resist Gardevoir. Don't think that just because the enemy has a Garchomp you can beat it with a Gardevoir. Garchomp can easily OHKO your Gardevoir with a single earthquake. You also need good coverage to fight against the inevitable steel, poison, fairy, and fire types. Furthermore, if you're thinking you need to switch your Gardevoir in and out of combat a lot, you have to get someone to remove hazards such as poison spikes, spikes, or stealth rock.
It might be wise to get a wish user as well as a reflect / light screen user as you're trying to buy as much time as possible for Gardevoir to recover.
Might also be more useful in doubles than singles. As in doubles you can use team protecting moves to defend during the recovery.
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By the way, I have fought Mega Gardevoirs and Sylveons before who've used hyper beam. I didn't realize at the time they were using pixellate but it was never a problem to deal with them.
After all, every single time I see Gardevoir or Slyveon appear, I usually just stall for one turn. So I would do a protect or I would switch with a steel type just to see what they would do. Since they both selected to use the hyper beam bomb, they were stuck the next turn which meant I easily destroyed them.
You might want to watch for that. If the enemy you're fighting has something that can resist the hyper beam and they switch it in when you use it... you're kinda fucked.
Furthermore, let's say you did kill the target. Now you can't do anything and the enemy switches in a... Lucario. He then uses that free turn to use a swords dance. Next turn he kills you in one hit with a bullet punch. What on earth do you do now? Lucario is 2x powered for free. That's another threat you have to watch for.