Hi @matt-seligman
You need to pass the ID of the category where the image is located. If you add the image to a category with the ID of 1, for example, you need to use this code:
$cat_id = '1';
the_field('image', 'category_' . $cat_id);
Or:
the_field('image', 'category_1');
This page should give you more idea about it: http://www.advancedcustomfields.com/resources/get-values-from-a-taxonomy-term/.
I hope this helps.