Well for him dying you could have be in a twisted way like in that one Batman the animated series run where joker kidnaps robin and pretty much makes him go insane and when told to shoot batman he shoots and kills the joker.

But honestly i wouldn’t kill him. Maybe make it like it seems that hes dead but really hes still lurking in the shadows twisting things or have in like in arkham knight where hes dead and hes inside batmans mind basically just torturing him and making him go insane.

But if you were to kill him have it where he does it to almost prove a message. Like the final stage they could fight on top of Wayne tower or something and when batman beats him he goes falling over the edge but batman catches him. (you could have it where batman is badly wounded from previous stages) and hes struggling to help him up but then joker flips it around and knocks himself out of batmans hold and falls down from the top of the building laughing. Then lands on a gcpd car and everyone around is shocked and in disbelieve. Then cut back up to see batman and he believes it was him that killed the joker and he broke his one rule. Then there you go you could even make a sequel game.