Thanks for the pictures.
The 7805 has 1uF, but it's better to add extra (ceramic of other fast) 100nF capacitors on both sides.
But the 7805 is noisy. Using it for a mic-preamp will always be a problem.
The noise for the ATtiny is not a big problem, but the noise for the mic-preamp is a larger problem.
You could try to filter the voltage for the mic-preamp and for the mic.
A few remarks:
The LM386 is an amplifier for a speaker, it's not very good for a mic.
You detect the peak and use 10uF with 2k2. That would make it impossible for a good FFT.
The inputs of the optocouplers need an extra resistor.