How about this?
It is missing a bypass cap from pin 3 to ground, I'd guess about 0.1uF will work.
Edit: dunno why that would not load as an image, try it as a link. It is just the schematic from the link above.
The problem with an LM358 is that it isn't great at approaching Vcc. Runs out of steam about 1.5V below it.
Just about any reasonable rail to rail Op Amp will work. You aren't building a mixing console, so noise isn't really an issue.
You are only interested in the waveform envelope, correct? The LM358 inputs can go down to ground, as can the output. So wire it up with ground as the reference, inverting amplifier. The Op Amp will only amplify the negative going part of the mic output, only going positive for them. Up to 3.5V on 5V power. Send that through an RC smoothing circuit, it'll end up being a max of about 1.5 to 2V. Now use the internal 1.1V analog reference. Adjust the microphone preamp accordingly.
Oh, yeah, lots of bypass caps on Vcc. Maybe even an RC network on Vcc to the Op Amp Vcc.