Ah! you need to pass the ‘options’ parameter! code below should work.
<?php while(has_sub_field('top_links' , 'options')): ?>
<li>
<a href="<?php the_sub_field( 'link_url'); ?>" target="_blank">
<img src="<?php $image = get_sub_field('link_image'); echo $image['url'] ?>" alt="<?php the_sub_field('link_name') ?>">
</a>
</li>
<?php endwhile ?>
edit: updated the code to add the alt tag (using the link_name sub field)