Printing field item attributes with Twig / Drupal 8
The syntax to print the alt tag in that case is this:

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


Twig in Drupal 8 doesn't deal with hash keys like #item in render arrays cleanly. Part of the problem is that # signifies a comment in Twig, so {{ item.#item.alt }} wouldn't work. 

There is the possibility of working around this with a Twig extension to allow drilling down into hash attributes with the syntax {{ item.item.alt }} but I'm not sure if anyone is working on that. I should mention that Twig extensions can be added in contrib as well.