WooCommerce: How to insert filtered attribute(s) in page title of archive?

You will have to add the variable ?filter_color to your title tag.
Something like this-

<?php
    $filter_color = $_REQUEST['filter_color'];
?>

This line of code will get the value from the URL.
(Make sure this line of code runs before the HTML where you want to output it)

And then in your HTML it should look pretty much like this-

<?php
    if( $filter_color ) {
        echo '<title>'. &filter_color .' Shoes</title>';
    }

    else {
        echo '<title>Shoes</title>';
    }
?>

Here we checked weather there was a variable set for filter_color or not and adjusted the output accordingly.