Just messing with this story. Basic idea stolen from +GinsuBastard (YouTube person) and I took the idea and ran with it to end up with this semi-written story...

At Arkham Asylum:

Batman walks to Jokers cell.
Batman: (demanding) where is he?
Joker: where's who?
Batman: I don't have time for games, I need to find Killer Croc!
Joker: killer croc....killer croc...that rings a bell. A towering figure? Green scaly skin? Sharp teeth and bad breath?
Right behind you...
-Joker smiles and laughs-
Killer Croc: it's time to kill the bat

Killer croc slashes Batman, pushing/forcing him to the wall.
Killer croc proceeds to destroy Batman.
The Joker is in cell with villainous smile and the shadows of what is happening goes on him. As it progresses, Jokers smile soon turns into a straight face. Realizing there is no more Batman.
Killer croc opens all the doors at Arkham Asylum announcing, the Batman is dead.
All the criminals escape while Joker slowly walks out in dismay.

Batman finally died at the hands of Killer Croc. The Joker, is all but happy about his rivals demise. With the world now realizing the Batman and Bruce Wayne suddenly gone, they soon make the connection. With the Robins gone and on their separate ways, Joker raids his house in anger, destroying whatever he can find and stumbles across Bruce Wayne's batcave with the grandfather clock he broke being the door. His eyes grew as he sees cave. He starts looting everything he can find.

He puts on his suit, insanely playing with the bat gear. Pretending to be Batman.
However, bored and dismayed, the Joker has no need to cause chaos. He looks in to the mirror and sees himself in the costume, realizes there is an imbalance and takes on the mantel of Batman. One that isn't shy of cheap tricks and killing. He now parades the night coming up with sadistic ways of capturing and often killing criminals.

The Jokers applies Bruces no kill rule only to Killer Croc. He sees him as a new "playmate". Knowing full well Croc would escape anything and wreak havoc, he sees the balance of calm and chaos they can make. A new villain to a new hero.

Harley Quinn is confused by the new path the former Joker has taken. (I think I want to make her a villain in her own right, but not sure how to go about that. Making her a "Robin" would be weird and almost obvious).

Dialogue between Nightwing and Joker.

Nightwing: What kind of sick twisted game are you playing? You have no right to wear that cape!
Joker: Go back to Bludhaven. You're of no use either. You're in more danger now than you have ever been...Dickie boy...
-Nightwing w/shocked expression-
Joker: After finding that Bruce is bats, it didn't take a great detective to figure that those kids of his were at one point a Robin of sort. I wouldn't be surprised if the butler, old Alfie, joined the fray.
You're compromised, all those villains you helped put away, all those who escaped will be after you.
I'm your ace in the hole. I masquerade as Bats and no one would know the better.

-News reporter in front of a Batman statue-
Reporter: with last week's death of Batman, who we now know is billionaire Bruce Wayne, civilians begin to honor him by taking up the mantel of the caped crusaders. This action, however noble, has resulted in 5 deaths and 3 fatally wounded Batmen. Commissioner Gordon insists that no one play vigilante and call the police when you see trouble.

-Zooms out the TV to Joker watching it-
Joker: pfft...amateurs. They don't realize the finesse! They just go in guns blazing not even thinking about the next move. Bats was always a step ahead, much like me. It was a chess game that we played into a stalemate. He had a plan to take out everyone in the room. And that mustard yellow belt had everything he needed.

Anyways...someone needs to run further with this idea. I think there's something here, whether it be a comic, YouTube movie, or YouTube series. Just throwing this out there, maybe it'll inspire someone. I'm surprised I put a lot of this together though, I'm a superman fan haha