If I use Fantina and then my Flying Pikachu V with Big Parasol attached uses its "Fly" attack and successfully lands heads, would my opponent's Giratina V's "Shred" attack do any damage to Flying Pikachu V or not?
Shred isn't affected by "any effects on the Defending Pokemon"; so the effects from Fantina and Big Parasol and Fly would all be ignored, and Shred would do damage.
FlyShredBig ParasolFantina