Suggested by IKnowledge Akiza has a good array of monsters on her side. Quite a few of them are very dangerous like her iconic dragon. Joker is a pretty decent fighter as he’s gone hand to hand against Batman at times. That being said, it’s certainly not enough to beat a dragon and Akiza also possessed telekinetic abilities of her own. That’ll make it very difficult for Joker to approach her at all and he’ll really be kept on the defensive. He just doesn’t have any way to approach her and his attacks won’t get through her bodyguards anyway. Akiza wins.
DReager1.com 
I still think Joker has a chance. Aside from his Emperor Joker form, if his bullets can go faster than cards, Akiza has a chance of this happening to her: https://cdn.bleedingcool.net/wp-content/uploads/2016/03/BKJHC-018.jpg, or dying from such an attempt. If that worked out, then the Joker would probably repeat what he also did here: Either way, Akiza would be affected beyond insta-repair. Just my two cents.
I removed the second link since it’s a little intense, but either way I don’t see Akiza going down like that. Remember that she has telekinetic abilities so bullets won’t be able to hit her. Not to mention that her cards are already on the field so she’ll be able to block any weapon that Joker can throw at her.