Chealion's answer works, and I'll be marking it as the accepted answer, but I figured out another way to do this also, cause I'm too impatient to wait for answers:
- Create a new set of settings with the desired level of opacity in
Terminal
-> Preferences
- Make the desired terminal window active and Show Inspector for it:
Shell
-> Show Inspector
or Command+I
- Choose the Settings tab in the Inspector and select the new set of settings. Viola! That one window is now transparent, without affecting the others that were started with the same set of settings.
The reason I wanted to do this was so I could put this window on top of another window that had similar (but not identical) output and visually inspect to see the difference. Consider the following:

vs:

It is much easier to quickly glance at the screen and spot the difference between the two.