You must have at least 0.1 uF bypass capacitors across each battery and another one placed directly across the op amp power pins. Better, use a parallel combination of 10 uF (observe polarity) and 0.1 uF across each battery.
There is no reason to power the mic from the noisy Arduino power supply. That may be where some of the noise is coming from, so use the positive battery supply terminal instead.
Finally, consider using just one battery, with a voltage divider to set "virtual ground" as described in this post.