Before we begin, I'd just like to state that you should use the highest level Pokemon you have along with the Pokemon I'm about to suggest. Pokemon with Damp are ideal as they are immune to Mind Blown, but anything will work, really. With that out of the way though, lets get on with the strategy!
So starting off, you should get a Hazer that should be able to prevent Mind Blown, while also being able to tank a couple of Blacephalon's attacks. I think an excellent candidate for this would be my pal Quagsire, as it takes virtually no damage from Fire Blast, prevents Mind Blown with Damp, can remove the +2 Sp. Atk increase that Blacephalon has with Haze, recover with Recover without using up too many healing items or instead wall Blacephalon with Amnesia, put it to sleep with Yawn, and even trap it into using Mind Blown or Trick with Encore! Quagsire can also be found at level 60 in the Ultra Space Wilds, so it requires 0 level grinding, as it would be an equal level to Blacephalon.
Quagsire @ Leftovers
- Recover / Amnesia
Next up should be a Pokemon that can prevent Mind Blown altogether for the rest of the team, while also helping the capture process easier by making it so that Blacephalon will also be easier to catch. I'm thinking of using Sigilyph, as its fast enough to Skill Swap Magic Guard onto Blacephalon, while also having decent bulk. Its got Thunder Wave to make catching easier, Roost for recovery, and provides some Sp. Def bulk for the team with Light Screen. Sigilyph can also be caught in Ultra Warp Rides too along with Quagsire, so there's no need for leveling up it either. Also note to safely switch in Sigilyph while Blacephalon is asleep, as it will likely be OHKOed by Shadow Ball
Sigilyph @ Light Clay
Ability: Magic Guard
IVs: 0 Atk
- Skill Swap
- Thunder Wave
- Light Screen
Now that Blacephalon has no Sp. Atk buff, doesn't take damage from Mind Blown, and is paralyzed, its about time you try catching it! I suggest you switch into either a high level Pokemon or just Quagsire in order to completely wall Blacephalon, and start trying to capture the thing. Use healing items when necessary, and that's basically it. Unless you run out of Beast Balls or something, your Shiny Blacephalon should be safely obtained.
As a side note, you should totally nickname the shiny Ronald McDonald because of phunni.