To start this mission you have to fly to the Joker's plane (picture).
In the first part of mission you will have to destroy enemy choppers and underbelly points of plane (picture) - they will be marked. You don't have to worry about getting hurt because Superman is resistance for normal weapons.
After first sequence Batman and Superman will land on the plane. Use Batman's rope on the oranges handles on the left and right side of the entrance and after that use Superman's laser on golden plates (pictures) - two of them are near entrance and other two are higher so you will have fly toward them.
When you enter to the plane use hook on the orange point on flying vehicle and after that use laser to take out the pilot (picture). Move Superman to the lest wall and link all pipes in one piece. Then outfit Batman in electrical suit which will shows on the left side and use him on the electric device on the right.
Now move to the top right corner and use electric current on the device (the platform will lower) Move up and use both heroes to hang on two levers (picture). When the gold wall will show use Superman's laser on it.
The next area is filled with kryptonite. Use Batman to destroy all four red devices near the walls (picture) and use bricks to build platform which will deactivate effect of kryptonite. Now move Superman to the door and pull the handle.
In the next area take down the flying machines (pictures) and get into one of them. Use rockets (press K) to destroy all silver bricks in the room.
Get out of the vehicle and use bricks to build two cranes and valves. Turn them (picture) and when the cranes take out the rocket use laser at the gold point. This action will destroy big doors in front of you.
In the next location you will have get on the higher level of the plane. Use Superman to fly there (picture) and eliminate some opponents. Pull the handle and when the bricks fall out use them to build platform with bat suit for Batman.
Take it and go to the blue wall on the left (picture). Destroy it with pistol, get to the fan and when you reach the top destroy blue part of the floor and jump into the hole.