The img_caption_shortcode example from the WordPress codex is a good skeleton structure to jump off of to add custom fields and adjust the markup to suit your needs.

In the following example, my ACF field is called “photo_credit” and is connected to any image file in the media gallery.

This will allow you to display additional information automatically (similar to a caption).

Targeting a media item

Something to keep in mind when getting custom fields that are attached to something like a media file is that you’ll need to pass a second parameter to target the media it is connected to.

One way of getting this corresponding ID is to use preg_match & regex to split the number off before the $attr are defined in the example below.

/**
 * Customize <img> shortcode markup..
 */
add_filter( 'img_caption_shortcode', 'my_img_caption_shortcode', 10, 3 );
function my_img_caption_shortcode( $empty, $attr, $content ){

	preg_match( '/(\d+)$/', $attr['id'], $matches );
	$media_id = $matches[1];
	$credit = get_field( 'photo_credit', $media_id );

	$attr = shortcode_atts( array(
		'id'      => '',
		'align'   => 'alignnone',
		'width'   => '',
		'credit'  => $credit,
		'caption' => '',
	), $attr );

	if ( 1 > (int) $attr['width'] || empty( $attr['caption'] ) ) {
		return '';
	}

	if ( $attr['id'] ) {
		$attr['id'] = 'id="' . esc_attr( $attr['id'] ) . '" ';
	}

     return '<div ' . $attr['id']
     . 'class="wp-caption ' . esc_attr( $attr['align'] ) . '" style="max-width: ' . ( 10 + (int) $attr['width'] ) . 'px;">'
     . do_shortcode( $content )
     . '<p class="wp-caption-text">' . $attr['caption'] . '</p><p class="photo-credit">' . $attr['credit'] . '</p></div>';
}

Additional Reading:

• WordPress Codex: img_caption_shortcode
• ACF Docs: Adding fields to media attachments
• php Docs: preg_match