Access image alt attribute in field template
With twig a preprocess function won't be necessary to get at this data (yay). Unfortunately we still have some weird "drupalisms" to deal with due to the render API. At any rate, here's how you get to it:

{{ item.content['#item'].alt }}


And here's the issue on d.o accounting for the drupalism (linked directly to comment with the above solution and explanation): https://www.drupal.org/node/2160611#comment-9358305