How can I adjust additional cinema display screen's brightness?
It's way simpler than that guys. The brightness on the display is controlled by simply pressing:

Control+F1 OR Control+F2 to adjust brightness on your secondary screen (the one without the menubar).

F1 and F2 to adjust brighness on your main screen (the one on which the menubar is located).

If you have adjusted settings in System Preferences for the Function Keys to behave as standard Function keys, you will need to hold the Fn key in addition to each combination too.

If your Cinema display has a USB cable (older models), you will need to plug it in.