Ok, this looks a little more like what you need. The supply here however is single ended, so polarity of the LED will come into play.
You have a full audio range (and then some) amp here, with all the basics to get you the output you're looking for.
The half of the op amp that's driving the LED has a fixed gain of about 30, and the preamp is set up with a gain of anything from unity to approaching infinity (not actually possible, but high enough to get the LED to light up, for sure!). In a nutshell, yes this thing is very sensitive if you need it to be.
You may find that you probably don't even need the 386 at all, since it's primary purpose is to drive the speaker. U1b simply taps off of the output of the 386 as it's input. While it may be providing the extra gain that the LED could need to see useful flashes of light, it's probably not necessary, and U1b (as drawn in the top schematic) can probably be connected to the "volume" pot's wiper directly instead.
If this isn't clear, let me know, I'll see about scribbling up a quick schematic.
Steve