2 loops in archive.php (one for each category)

Just switch conditionally. The rewind_posts() function allows you to loop through the same loop a second time, while the has_term() function allows you to check if the currently looped post has a specific term of a specific taxonomy.

if ( have_posts() )
{
    while ( have_posts() )
    {
        the_post();

        if ( ! has_term( 'term_A_slug/term_A_id', 'taxonomy' ) )
            continue;

        // display post here
    }
}
rewind_posts();

// Second loop
if ( have_posts() )
{
    while ( have_posts() )
    {
        the_post();

        if ( ! has_term( 'term_B_slug/term_B_id', 'taxonomy' ) )
            continue;

        // display post here
    }
}