How do you beat a Shedinja in an Inverse Battle?

Question

how do you defeat a shedinja in an inverse battle?

Answer 1

Hit it with moves of the following type;
Normal
Grass
Fighting
Poison
Ground
Bug

Those types are the ones ineffective against Shedinja's Bug/Ghost typing, ignoring Wonder Guard. Factoring it in and Inverse battles, those ones are the ones that will kill it.
In addition to this, most of the old techniques worked - Mold Breaker, Gastro Acid, TurboBlaze etc. as well as Weather, Hazards and Damaing Status.

Answer 2

Easily! Shedinja gains a weakness to Bug, Ground, Poison, Grass, Fighting and Normal type attacks in Inverse Battles, so any move of that type will break though Wonder Guard be able to hit Shedinja.

Like with every other Pokemon, Shedinja's weaknesses and resistances are swapped during Inverse Battles; Wonder Guard does not make it an exception to this. Basically, everything that is normally immune to hits it for super effective damage during Inverse Battles, and anything that is ordinarily super effective on will not do any damage to it during an Inverse Battle.