Diode Only
https://d.top4top.io/p_15225cuuz1.jpg
OK... That will protect your Arduino from negative voltages but with no current limiting (no series resistor) you might burn-up the LM386.
...With a 4 or 8-Ohm speaker attached, you'll get a voltage drop across the resistor and depending on the resistor value you probably won't get enough signal. If you have a speaker that eliminates the need for the pull-down resistor, but the pull-down should have much-higher value than the series current-limiting resistor.
But like I said, the LM386 has too much gain. Leave it out!
This isn't that hard... You've been given 2 easy solutions - The normal bias circuit (2 equal value resistors and a capacitor) or the protection circuit (a series resistor, a diode*, and a higher-value parallel "pull down" resistor).
Your audio signal into the Arduino doesn't need to go all the way to 5V. You can adjust meter sensitivity in your software. The 10-bit ADC has about 5mV resolution with the default 5V reference (1023 "steps"). Or if you are using negative-protection instead of bias you can use the 1.1V reverence for about 1mV resolution. Or, you can use a different externally supplied reference. Or, you could use a pot for an adjustable reference to adjust the sensitivity or to "calibrate" your meter.
Or, you can make a peak detector with an op-amp (not the 386) which can optionally have some gain. But that's more complicated and for optimal performance it should be powered with positive & negative power supplies, the positive power supply voltage should be greater than +5V so it can go all the way to +5V (slightly over, actually) and it should have an over-voltage protection circuit (this time to protect from higher positive voltages).
I wouldn't recommend a peak detector until you get one of the easier solutions figured-out. 
* Ideally, the diode should be a Schottky type if the series resistor is less than 5 or 10K. There are already "little" protection diodes (standard silicon diodes) inside the Atmel Atmega chip and those tiny internal diodes are only rated for 1mA. With a similar external diode you can't be sure where the current is going and there is a chance of damaging the one inside the chip (and possibly doing other damage).
A regular silicon diode has a forward voltage of about 0.6V and a Schottky diode has a forward voltage of about 0.2V so with a Schottky in parallel the internal diode will never "turn on" and all of the current will flow through the (higher-current rated) external Schottky diode.