Archive.php filtered by pre-determined category

add_action( 'parse_query', 'wpse_60354_archive_category' );
function wpse_60354_archive_category( $wp_query )
{
    if ( $wp_query->is_archive() )
        $wp_query->set( 'cat', ID_OF_CATEGORY );
}

Just replace ID_OF_CATEGORY with the ID of your category, obviously 😉