It is not possible yet to search for content using multiple tags, for now only single tags are supported.
Firstly, the Instagram API endpoint "tags" required OAuth authentication.
This is not quite true, you only need an API-Key. Just register an application and add it to your requests.
Example:
https://api.instagram.com/v1/users/userIdYouWantToGetMediaFrom/media/recent?client_id=yourAPIKey
Also note that the username is not the user-id. You can look up user-Id`s here.
A workaround for searching multiple keywords would be if you start one request for each tag and compare the results on your server. Of course this could slow down your site depending on how much keywords you want to compare.
