When you beat the game, you unlock several things. It doesn't matter which difficulty.
The second booby trap is a lot simpler. You will first notice a vase. It does not need to be broken. Past it you will see two paths (left and straight). Go to the left. At the end of the hall is a door guarded by motion sensor. Trip them, then run to the left or right wall along the hallway. A painting should slide up, revealing a mini gun prepared to spray the door on the opposite side of the motion-sensored door. Above the painting is a grate. Grapple and wait for the intermission sequence. A man will come out of the locked door. Finish him with the static type of attack. Drop and go into the room that the man came out of and kill the unarmed man. Look for the button to open the door which was shot at, and the door will be unguarded and unlocked.
You'll be able to play through the game with some old batman suits which are all unlocked at the same time