Objective 1: Activate the Drill
Smash the Lex Luthor prop to the southwest of the start of the level.
Lex Luthor Smash Challenge: 1 / 3
Cross the bridge and jump onto the rocks to the left. While standing on the tallest one, equip Batman with the Demolition Suit and fire a missile at the silver LEGO on the drilling rig. The drill roars to life and spits out some bricks.
Jump across to the drilling platform. Here, you find another Lex Luthor prop to the left.
Lex Luthor Smash Challenge: 2 / 3
Objective 2: Find the Jail Cells
Use the bricks that came out of the drill to build hyper strength handles on the nearby gate. Have Solomon Grundy pull on the handles to rip the gate open.
Pass through the now-open gate and equip Batman with his Sensor Suit. Inspect the green LEGO wall to the north while your partner throws the switch and turns the valve next to it. The machinery springs to life, aligning a bridge nearby. Head right to cross the bridge to a platform full of goons.
Once the baddies have been wiped out, scan the platform with Detective Mode to locate a computer terminal.
Have Robin hack the computer to align the platform and its bridge to access the southwest side of the mines.
Cross the bridge to the southwest to find the Red Brick sitting in the open.
Red Brick
Objective 3: Free the Prisoners
Continue onward to the east and you arrive at some jail cells. Have Wonder Woman take control of the prisoner in the leftmost cell. Now under your control, have him smash the Lex Luthor prop. With that out of the way, have him smash the nearby rocks and build the LEGO bricks that spill out into a switch. Throw the switch to open the cell and the one to the right.
Lex Luthor Smash Challenge: 3 / 3
Take control of the prisoner in the rightmost cell and have him smash the rocks. Build the bricks into a switch that opens his cell. Now the three prisoners can destroy the boulder in the center of the prison area. Jump into the hole left behind to exit the level.