Gold Brick #1
You'll acquire this as part of the story, when Plastic Man confronts Mr. Freeze.
Gold Brick #2
Green Loontern appears on the lower platform of the main room. Speak to him to make some loose parts appear. Build them into a new teleporter to unlock a new area and earn a Gold Brick!
Gold Brick #3
Aquaman and Black Canary appear on the right side of the main room, where Aquaman needs help restoring Canary's voice. Head to the middle of the room and use a demolition character to blow open the silver chest there. Switch to a sonar character to shatter the glass case inside, then bring the shell it was holding back to Aquaman to finish the quest.
Gold Brick #4
Kevin Smith can be found in the Containment Cells, and when you talk to him, Condiment King will show up. Defeat him and his goons to win a brick.
Gold Brick #5
Next in the Containment Cells is Killer Moth, who "hopes no one follows him" to his treasure. Follow the trail of studs to some lightbulb switches. Step on them all to guide Moth to his stash: a Gold Brick for you.
Gold Brick #6
You'll find the oblivious Booster Gold in the Laboratory. He wants someone to dress as him and beat up bad guys. To do this, make a custom character with the Booster Gold helmet and body and speak to him to earn a Gold Brick.
Gold Brick #7
Gold Brick #8
After completing his first quest and beating up the goons that show up, Booster Gold can be found out in the main room, lamenting the fact that his copycat has outshone him. Head to the "Bronze" sign behind him and bust up the equipment underneath for some loose parts. Build these into a magnetic awning, then use a magnetic character to change the sign to say "Gold." This completes the quest.
Gold Brick #9
Catwoman can be found in the Trophy Room, and she wants you to steal a cat statuette for her. Head to the upper level and destroy the silver box with a demolition character to reveal a handle, then pull it to kill the lasers around your prize. Return it to Catwoman to finish the quest.
Gold Brick #10
You'll find Man-Bat on the upper left side of the Hangar. He needs your help finishing his new formula; you need to find a green flask. Check the other end of the platform for a bunch of flasks on tables, then bring the right one back to Man-Bat to receive a brick.
Gold Brick #11
For the last quest, talk to Batgirl in the hangar. She'll tell you about some civilians Harley Quinn trapped in boxes. Bust them all up (some contain enemies) and lead all four civilians back to Batgirl to complete the quest.
Gold Brick #12
In the main room, there are five signs above each doorway. Shoot them all down (they take a few shots each) to earn a Gold Brick.
Gold Brick #13
In the Containment Cells, head to the right to find three penguins trapped in beams. Pull all three levels before time runs out to free them and win a minikit.
Gold Brick #14
In the Laboratory, look near the character customizer for a tech panel. Use a tech character on it to reveal a glass case on the lower platform. Shatter this with a sonar character to grab the Gold Brick inside.