AFAIK the closest you can get is transferring Sturdy to Shedinja, then paralyzing it yourself, while it holds the Safety Goggles. Since Shedinja only has 1 HP, it will always have full HP for Sturdy to make it survive a hit with 1 HP. Because it's paralyzed, it can't be Burned, Poisoned, or Toxic'd. And the Safety Goggles will protect it from Sandstorm.
The issue is actually getting Sturdy on there in the first place, since Wonder Guard is an otherwise sort of OP ability. GameFreak made it not possible to transfer while it's active. So you need to suppress it or override it first, with things like Gastro Acid or Worry Seed. In Double Battles, this is kind of a death sentence, since you leave your Shedinja vulnerable to all forms of damage for a full turn before you can move Sturdy from the other Pokemon. The further problem being that, AFAIK, the only Pokemon capable of transferring Sturdy onto Shedinja is Carbink, since it learns Skill Swap and has the ability Sturdy. But... Carbink can't learn any ability suppressants -- it can only Skill Swap. So you have to survive an extra turn to swap the Carbink in after you've suppressed Wonder Guard. The math changes a lot on Triples, but those are kind of not a thing. Park Shedinja in the middle, between the Carbink from above, and an Eelektross on the other side that knows both Gastro Acid and Thunder Wave. Manipulate the Speed stats of the Eelektross and the Carbink so the Carbink will always move immediately after the Eelektross to minimize the possibility of your opponent interrupting the transfer process. Then, the next turn, use Thunder Wave to paralyze Shedinja, while you switch Carbink out for soemthing else. Like a Ditto, which can Transform into the Shedinja, for example.
Further, there's no way to stop item manipulation. Knock Off is very common, and even Trick to swap items sees a fair bit of use. Similarly, there's no way to prevent the Shedinja from being Confused, since Sturdy doesn't block damage from Confused. I think multi-hit moves also get around Sturdy, since it only triggers once per move use. And while you'll probably never see it in competitive play, Future Sight takes place between turns, where Sturdy doesn't take effect (like Burn/Poison/Toxic and Sandstorm).
