I think that I would argue that the AC is irrelevant. As with all illusions, the relevant point is whether or not the opponent recognizes it as an illusion or not, via their willpower saving throw. The rules on illusions state that when they interact with it "in some manner" they get to make the saving throw to disbelieve it. If they fail, the continue to believe it is real. It doesn't say that they have to hit it, only that they have to interact with it in some manner. I would rule that merely making the attempt to hit/attack affords the opponent that save, regardless of whether or not they might have overcome any particular AC with their attack. If they fail their save, then as a DM I would continue to act as if the foe believed in the illusion.
As a semi-related side note, the description also raises another interesting question. Since spells cast by the PC can originate from the shadow duplicate image, is a foe still affected by those spells that originate from the image?