Here's my description - I realized I couldn't draw storyboards fast enough (my memory is fading! Ack!) so I decided with a text description instead. I tried to focus a little more on camera angles than deathfromabove's description.
WB, Legendary Pictures, and DC logos fade away into a blue fiery smoke.
Sudden immense aerial view of a Gotham city block, brightly lit during the day. Camera slowly zooms in to focus on one building, that's made up entirely of windows. Suddenly a window blows out.
Cut to inside the building. A man in a clown mask levels a grappling gun to frame right, then fires toward the nearby lower roof of the Gotham National Bank. He secures the zipline, then plunges down it. Another clown-masked man does the same. The camera follows them out the window then swoops down to a dizzying view of the street below.
Cut to a waist-down back shot of a man standing on a street corner with his head down, holding a clown mask in his left hand. (This is the Joker, although the characters and the audience are unaware of it.)
We slowly pan up as a van approaches frame left. The man quickly puts on his mask and enters the right back door of the van.
Cut to inside the van. The camera is in the back, looking toward the windshield. The Joker has moved to the left back side of the van, and is loading a gun. The camera moves outside of the van, looking into the passenger side window. The two men sitting in the front, also wearing clown masks, discuss how there were supposed to be 6 people in on the job (there are 5), and how their boss expects a cut even though he isn't directly involved. "Must be why they call him the Joker!"
Cut to the bank rooftop. The two masked men move frame right as they approach a security wiring box, and discuss how the Joker wears make-up "like war paint" while jimmying the box open.
Cut to outside the bank, with the camera looking at the back of the van. The van stops camera left, and everyone exits frame right, going up the stairs while the camera moves with them. The Joker is the last to follow.
All three masked men enter the bank frame right, and one of them starts shooting into the air. They begin threatening customers and tellers, telling them put hands down. "Not hands up! Hands down!" One of them threatens a man cowering on the floor, and another drags a teller over the counter by her hands. The Joker has still said and done nothing.
Cut to the bank rooftop, the camera placed to the left of the security box, facing the two robbers. One of them is in the foreground, presumably messing with the wires. He notes how the alarm is now intercepted, although it doesn't go to 911, it goes to a private number. Almost unnoticed by the audience, the man behind him raises his gun slowly, then shoots his partner in the back.
Cut to the POV of the shooter, looking down at his dead partner, who has fallen to his left. The camera follows him as he moves down the stairs and meets with one of the van-arrived men who is trying to get the vault open (on frame right) with a drill. He takes the drill to the vault and is suddenly thrown back (frame left off-screen) by a large electric burst.
In the bank lobby, the 2 remaining men are prying open each hostage's hands and putting something into them. Close up of a robber placing a live grenade into the teller's hands. "We wouldnt want your hands free would we? Inside a windowed room, the bank manager turns and looks concerned, then angry.
Cut to the bank vault on frame right. The robber who was shocked now has his hands placed in his sneakers and is working on turning the vault door open that way. He exclaims how is it that a bank has a vault protected by 22,000 volts. His partner says that it's a mob bank. The vault-breaker asks about the man who was supposed to take care of the alarm. The other says he shot him dead, so they get a bigger cut, and that the Joker ordered him so. The vault-breaker gets the vault open, turns around and realizes his partner has a gun trained on him. He pleads, "No!" but his partner shoots him in the chest off-screen. The remaining robber takes his duffle bag inside the vault and starts sweeping cash into his bag.
Inside the bank, the camera follows one of the masked men, who notices the manager crouched low in his room and moves to take a shot...and the room explodes, revealing the bank manager holding a large shotgun under his desk.
He jumps out of the hole in his room and starts blasting at the robbers. He makes it clear that they have messed with the wrong bank - the money belongs to the mob. They're as good as dead.
The vault robber arrives, just as the manager starts shooting at him. He ducks behind a counter. The Joker hides behind a counter, then manages to crawl to where the other robber is waiting. The other man asks the Joker if the manager has run out of shells. The Joker, cowering with his arms wrapped around his knees, meekly nods yes. The other man immediately stands up in the foreground to take a shot. The manager blasts at him and he crouches back down. "Where'd you learn how to count?" he retorts. The Joker turns toward him with an annoyed movement. (He obviously wanted the other guy to get hit.)
Eventually the manager runs out of shells. Immediately, the Joker stands, then shoots and wounds him. The manager falls to the floor, still alive but writhing in pain.
The Joker and the remaining robber gather up the duffle bags of cash at the center of the floor. Then when the Joker has his back turned, the robber takes out his gun and trains it on him, saying, "I'm sure the boss told you to take me out first." The hand that is holding the gun is shaking just a little. The Joker looks unconcerned, and takes two smooth, theatrical, almost playful steps to his right, moving unperceptively away from the path of the door. "No, I'm supposed to shoot the bus driver," he says, shrugging nonchalantly.
The other robber looks confused. "Bus driver?"
Suddenly the door explodes frame right and the back end of a yellow school bus bursts into the bank, knocking over the robber with the gun. Another clown-masked man exits the back door of the bus and starts helping the Joker throw in the bags of cash. When they're almost done, the Joker turns away and coolly shoots the last robber in the chest.
The bank manager has seen all of this, and mutters how they used to believe in honor in Gotham's underworld. He demands of the last robber (the Joker), "What do you believe in?" The Joker, after throwing in the last bag of cash, turns curiously to the bank manager and tilts his head slightly. The camera follows as he saunters over to the bank manager, still lying prone on the ground. The Joker gently places a cylindrical grenade into the manager's mouth. The grenade is attached to a string. The manager's eyes go wide. The Joker speaks. "I believe that what doesn't kill you, makes you..."
Camera cuts close-up to face the Joker as he lifts his mask, revealing a face ruined by blotchy white makeup and a large scar on his mouth. "...stranger." He gives the manager a brief wide, mischievous grin, then puts the mask back on and the camera follows as he walks back toward the bus. The end of the grenade string is attached to his belt loop. The manager shudders slightly as the string tightens.
With the camera facing the back of the bus, the Joker closes the door on the string, then moves out to the front to drive it out. As the bus rolls away, the camera focuses on the bank manager, as the grenade string is pulled taut and is finally yanked out of the grenade. The manager's eyes go wide for a few suspenseful seconds. Finally, a short "pffft" as a gentle smoke is released from the end of the grenade. The manager's eyes roll back in his head in relief.
The bus containing the stolen money rolls out of the bank frame right. Clouds of dust fall off the end. The bus merges onto a city street in between 2 other equally yellow school buses, driving away from camera. Police cars, with their sirens on, start to approach the bank toward the camera.
Cut to a frontal shot of the new Batsuit in a wooden cage.
Cut to several shots of Batman riding the Batpod at night. Shot of the black Tumber rounding a curve frame right.
Cut to a nighttime waist-up shot of the Joker looking toward frame right, pumping off several rounds with a large gun. He's not smiling, but in total concentration.
Cut to a group of policemen surrounding the Batsignal during a cloudy day (the audience cannot see that it is the Batsignal - it's just the floodlight portion). Jim Gordon stands in front. He slowly raises an axe.
Cut to Batman standing on top of a very tall building (Sears Tower), with his right hand to his ear. It almost looks like he's saluting, except he looks deep in concentration. I don't remember this shot being at night - it's at dusk, most likely.
Cut to Gordon bringing down the axe. Camera cuts to face directly into the batsignal. The axe comes down, and the symbol shatters.
The new, black, sleek, blue-tinged Bat symbol fades into screen.