The strategy with the greatest rewards, but also has the greatest risk, is to use it in Triple Battle with a combination of other Pokemon. However, using it this way will dedicate at least 2 other Pokemon to setting it up.
Shedinja @ Safety Goggles
Ability: Wonder Guard
EVs: 252 Attack, (any)
- Hone Claws
- X Scissor/Skitter Smack
-Shadow Claw/Phantom Force/Poltergeist
This is your centerpiece. It should be in the center of your formation, and you should, ideally, never remove it from the field after it comes out. Safety Goggles will protect Shedinja from Weather, one of the primary ways to bypass Wonder Guard (that said, we won't be keeping Wonder Guard long). Now, onto the support crew.
-Thunder Wave (prevent Shedinja from being Burned or Poisoned)
- Gastro Acid (neutralize Wonder Guard for replacement)
- Skill Swap
You might already see where this is going. Ideally, you'd manipulate the Speed stats of both Eelektross and Carbink so that they are just slightly off from being the same -- the goal is for Eelektross to get it's turn immediately before Carbink does. The reason for this is to minimize the period in time where literally anything can destroy Shedinja, because Wonder Guard will be turned off.
Turn 1, Eelektross uses Gastro Acid, to neutralize Wonder Guard, to allow for Carbink to use Skill Swap in order to replace it with Sturdy. Hopefully your opponent hasn't used a Dark or Fire type move to obliterate Shedinja before this point. Meanwhile, Shedinja should be using Hone Claws.
Turn 2, Eelektross uses Thunder Wave to paralyze Shedinja. This will prevent you opponent from using Will O'Wisp or Toxic to Burn or Poison Shedinja. If you have reached this state, it becomes almost impossible for your opponent to KO Shedinja.
If you really want to add insult to injury, switch Carbink out and replace it with a Ditto, and have it Transform into your Shedinja. That would be Turn 3 at the earliest, by which time Shedinja should have used Hone Claws at least twice, maybe even 3 times depending on the opponent's team comp and actions. This would mean you now have 2 Shedinjas with Sturdy and +3 to both Attack and Accuracy (but only 1 has Safety Goggles to protect from Sand/Hail). Further, Shedinja's (and now, Ditto's) movepool really doesn't have anything to effectively combat Water and Flying types, but since you have Eelektross... well, do the math.
That doesn't mean you've guaranteed a victory, though. Abilities that allow attacks to bypass other Abilities will destroy a Sturdy Shedinja. Item manipulation strategies can remove the Safety Goggles, making you vulnerable to weather damage. Your opponent may have brought a medic, in which case they may be able to cure your Shedinja of Paralysis, leaving it vulnerable to Burn or Poison. I'm unsure of how multi-hit moves will interact with Sturdy Shedinja. Normally, Sturdy can only take effect if the target is at full health, meaning the second hit would KO any other Pokemon, but since Shedinja would forever be at full health after each hit, it complicates things. It would depend on whether or not Sturdy can trigger multiple times per turn or not.