Chapter 1: Theatrical Pursuits
Once you have controls, you can destroy several objects here to gain some studs but I do suggest to just play normally until you have the chance to gather the multiplier blocks, which can easily and quickly rack up your score.
Head in front of the stage and hold B to reconstruct the blocks. Next, you have to hit Harley Quinn with your batarang. To do this, hold the X button and move the reticule until it locks on your target. Use the minions to replenish your hearts. It will take three hits to defeat Harley.
Collect the remaining studs if you want, then jump down the trapdoor. Use the savepoint then continue. Continue hitting the large metallic piece to your immediate left until it destroys the wall to the right and reveal the Riddler inside. Continue destroying the pieces here to earn more studs.
Head to the right to reach the next area. Press and hold X and target the highlighted grappling hooks. Upon reaching the ledge, grab and hold one of the grappling hooks then switch to your next character and do the same to jump to the other ledge. Continue along and push the lego piece so it shatters on the ground.
Jump down and assemble it so you can change into the Sensor Suit. Press and hold the B button to activate stealth mode then go past the security camera and defeat the henchmen controlling it.
Mini-Kit and Sensor Suit
Continue to the next room and use both characters to grab the grappling handles and hold unto them to open the next room. Stand in front of the green board with the Sensor Suit equipped and press B. Find the riddler and press X to hit him. Do this three times to make him appear. Defeat him then re-assemble the green pieces and ride the lift to continue.
Destroy the cart nearby and reassemble it to get the Robin Acrobat Suit. Switch to it then defeat the enemies that will appear. Press and hold X to place the pole and use it to reach the concourse area. You'll be facing Two-Face next.
First, destroy the planters near the railings and reassemble them so Batman can use his grappling hook and join you. Switch to him and go stealth to get past the security cams. Destroy the objects inside and reassemble them to turn into a switch. Switch to Robin and press and hold B to become a ball. Jump in the middle of the switch and move forward to activate the switch and lower Two-Face.
Defeat him easily using a stealthed Batman then use Robin's acrobat stick to reach the mini-kit to the upper right, near the ceiling.
Continue to the elevator and face the Joker. If he grabs one of your characters, switch to the other one to attack him. You may also want to defeat his annoying minions. When he's down to one heart, head to the green power panel and use Batman's Sensor Suit to fix the cables. Finally, re-assemble the broken lego pieces near the open wall and use the zipline to reach Joker.
Wiping that smug smile off
Next, you have to pursue Joker. First, jump down to ground level and head to your right. You should find some hopping red lego blocks. Destroy them all to reveal a gold brick.
Jump down and head to the left. Re-assemble the pieces on the yellow platform the equip the sensor suit. Next, head to the green panel and release all the red locks. Re-assemble the pieces then switch to Robin's Acrobat Suit. Turn into a ball again and jump on the mechanism like what you did earlier with your fight against Two-Face.
Re-assemble the piece to activate the terminal and use it call in Robin's Helicopter. Ride the helicopter to and watch the following scenes to start the next chapter.