-4 Ghost-types (i.e. Chandelure)
Okay, so the strategy is lead with Delcatty and Audino (both holding Focus Sashes). Audino uses Skill Swap on Delcatty to gain Normalize, Delcatty uses Fake Out/Protect to stall. Delcatty switches out to a waiting Ghost-type, such as Chandelure. Audino proceeds to use Entrainment on the opponents, giving them the Normalize ability. As all their moves are now Normal-type, nothing would touch Chandelure, and it could sweep without worry. Now this strategy would be PRIME if Chandelure had it's BW hidden ability, Shadow Tag, but alas, it does not in X/Y. You could even switch out to Wobbuffett or Gothitelle to utilize S-Tag. Would it still be a good strategy, or would it be too much work?
Yes that strategy would work although it would take some dedication to pull off. Audino has neough bulk that you can get away with running Leftovers for her. Although Delcatty will definitely need that Sash. Some much easier strategies to pull off in Doubles is Tailwind, DisQuake, and Trick Room, to name a few. Yours will work, but you have to have dedication for it, practice lots to work out potential bugs. For example Audino could get killed by a fighting move before it can use Entrainment. Taunt would render Audino incapable of using Entrainment. You might be up against two ghost Pokemon meaning that Delcatty could be double targeted. There are multiple potential scenarios that could happen making your strategy tough to pull off. It would work, but it's not foolproof unfortunately. It'd be much easier to make a Trick Room team to screw over your opponent's Pokemon.