This Achievement is unlocked by beating all five Acts of the third episode as Batman and Robin.
The final act has three main phases:
1. Get both Batman and Robin on top of the two platforms that will cause each bell to ring, dropping Harley Quinn and the Joker onto the ground.
2. Use the water cannon to hose down the Joker's helicopter, while dodging the machine gun fire that it rains down on you.
3. Battle the Joker in melee combat - if he is electrocuting one of your characters with the joy buzzer, just tap Y to switch to the other character and start punching. Repeat as necessary until he has been defeated.