How do I retrieve an image’s width and height using Advanced Custom Fields?

You can get the ID for the attachment with $attachment_id = get_field('field_name');. When you have the ID you can use wp_get_attachment_metadata() to get the info associated with the image in an array. The images width and height are stored in cells named width and height.

$attachment_id = get_field('field_name');
$metadata = wp_get_attachment_metadata($attachment_id);

$width = $metadata['width'];
$height = $metadata['height'];