[instagram-api] How can I get a user's media from Instagram without authenticating as a user?

11.11.2017
Since Instagram changed the way they provide this data, none of above methods work nowadays. Here is the new way to get user's media:
GET https://instagram.com/graphql/query/?query_id=17888483320059182&variables={"id":"1951415043","first":20,"after":null}
Where:
query_id - permanent value: 17888483320059182 (note it might be changed in future).
id - id of the user. It may come with list of users. To get the list of users you can use following request: GET https://www.instagram.com/web/search/topsearch/?context=blended&query=YOUR_QUERY
first - amount of items to get.
after - id of the last item if you want to get items from that id.