I would take a look at the “Simple Taxonomy Query” section over on the WP_Query WordPress Codex page. I’ve set things up on a few sites this way.
Source: codex.wordpress.org/Class_Reference/WP_Query
Wrap the link and image inside of an if, which checks to see if both are not empty like this:
<?php if ( get_field(‘field_link’) != “” && get_field(field_image) != “” ) { ?>
“>“>
<?php } ?>