Permalinks: custom post type -> custom taxonomy -> post

First, register your taxonomy and set the slug argument of rewrite to shows:

register_taxonomy(
    'tour_types', 'tour',
    array(
        'rewrite' => array( 'slug' => 'du-lich', 'with_front' => false ),
        // your other args...
    )
);

Next, register your post type and set the slug to shows/%tour_types%, and set has_archive argument to shows:

register_post_type(
    'tour',
    array(
        'rewrite' => array( 'slug' => 'du-lich/%tour_types%', 'with_front' => false ),
        'has_archive' => 'shows',
        // your other args...
    )
);

Last, add a filter to post_type_link to substitute the show category (types tour) in individual show permalinks

function hdev_show_permalinks( $post_link, $post ){
    if ( is_object( $post ) && $post->post_type == 'tour' ){
        $terms = wp_get_object_terms( $post->ID, 'tour_types' );
        if( $terms ){
            return str_replace( '%tour_types%' , $terms[0]->slug , $post_link );
        }
    }
    return $post_link;
}
add_filter( 'post_type_link', 'hdev_show_permalinks', 1, 2 );

Forgot the has_archive argument of register_post_type above, that should be set to shows.

Result: