Not really an "exclusive attack", but here's a link to the EX Battle with Kamen Rider Core. It's actually a three person team: Core, Ryuuga and Ouja (Well, Ryuuga and Ouja are the actual opponents, gameplay-wise, Core is just like an extra special card every turn).
[ame="http://www.youtube.com/watch?v=5T7i8nU1O2c"]YouTube - ??????????????????????????????[/ame]
Core also appears in the middle of standard battles, but he can't be defeated there, just attacks one of the players and leaves.
Here's an actual Ganbaride exclusive. Dark Kiva's Unlimited Blade Works!
Well, it's actually called "Extinction Zanvat Beheading" or something close to that. Kiva & Dark Kiva are actually the opponents of the Hyper EX Battle of collection 005.
[ame="http://www.youtube.com/watch?v=nKBOIfdJ20w"]YouTube - ???????????005????(??????EX??!)[/ame]