There are a few ffmpeg filters you can use with mpv to get this effect, though you may have to fiddle with their options to get what you want. acompressor or dynaudnorm might be what you're looking for.

https://ffmpeg.org/ffmpeg-filters.html#acompressor

https://ffmpeg.org/ffmpeg-filters.html#dynaudnorm

To use them with mpv you'd do something like `mpv --af=lavfi="[dynaudnorm=param1=value1:param2=value2:param3=value3]" ...`

(make sure the first parameter is preceded by a '=', not a ':' because reasons)