How to show Advanced Custom Fields data above share links, pagination, etc

Plugins typically insert their content via the_content filter. The filter runs when the_content() function is called, and passes the content through the filter before output.

Remember, with a filter, you need to append to the existing content, then return the results.

add_filter( 'the_content', 'wpd_content_filter', 10 );

function wpd_content_filter( $content ){
    if ( is_single() && get_field( 'review_score' ) )
        $content .= '<span class="review-the-score">' . get_field( 'review_score' ) . '</span>';

    return $content;
}

The third argument of add_filter is the priority (10 in the above example, the default). You may need to make this a lower number if plugin content is appearing above your own.