UPDATE 5/2020: Instagram can now be directly archived via archive.is. However, stories and multi-photo posts don't archive correctly so this tutorial still has some use for the time being.
Recently, the question came up about how to archive Instagram posts. https://voat.co/v/pizzagate/2862992/15133902 Currently, Instagram is set up so it can't be archived by archive.is, web.archive.org, or any of the search engine cache sites. However, there is a workaround. Many websites mirror Instagram in real-time or at a slight delay. You can then archive an Instagram post from one of those sites. Since the pizzagate thread above mentioned nununu clothing, I thought I would check how some of these sites differed by using the most recent nununu post: https://www.instagram.com/p/BqXg4nnn8Zm/.
For each site I compared the URL ending from the original Instagram post to the mirror site. The sites where the URL has the same ending are helpful for quickly archiving older posts. Most mirrors require finding the username or hashtag and scrolling through until you find the correct post. I also tried to see which mirrors supported the multi-picture posts, like this one: https://www.instagram.com/p/BqXg4nnn8Zm/. That URL is not listed in the chart, but my findings on whether or not the mirror supports it are.
The number of comments that appeared alongside each post was consistent for most sites. However, some sites showed different numbers of comments for each post. The posts with a greater number of comments showed more, but still not all the comments appeared.
April 29 2020: In order to make it easier on myself, some of the sample URLs from the newer sites do not use the original Nununun post. However, I still used images from Nununu clothing, as while they are disturbing on some level, they are not as graphic as many other pizzagate related images.
Based on the chart, here are my picks.
Overall, inkphy.com is the best. It is the only site that archives multi-photo posts and has matching URL suffixes. It only comes 1 short of the highest number of comments shown. If you need to archive who liked a post then go with Picsoro.com. Updated April 2020: My pick now is theinstaprofile.com / insta-like-viewer.com. In addition to the features in the original chart, these sites allow archival of stories. In addition, these sites allow posts that are not private, but a user needs to be signed in to see (stapico.com also has this feature). However, if you want to use URL endings (helpful for not scrolling through posts), my pick is Stagramer.com as it shows the largest number of comments.
Feel free to post in the comments any other mirror sites you find.
EDIT: Since @shewhomustbeobeyed and @Factfinder2 asked for more detailed instructions. I will try to provide them below.
First, find the Instagram post that you want to archive. For example, @carmencita suggested https://www.instagram.com/p/BZAreJnnkwW/
Second, open archive.is and paste in
https://inkphy.com/media/ https://stagramer.com/explorer/ Don't press enter yet.
Third, copy the ending of the Instagram URL. You will want to copy everything after /p/. In this case, you will copy BZAreJnnkwW/.
Fourth, go back to archive.is and paste the URL ending behind
https://inkphy.com/media/ https://stagramer.com/explorer/. The final URL will look like https://inkphy.com/media/BZAreJnnkwW/ https://stagramer.com/explorer/BZAreJnnkwW/
Fifth, hit enter and the page should archive. The final version looks like this.
If, instead, you use one of the mirrors that doesn't have matching URL endings, the process won't be as simple.
First, you will have to find the post. Many of the mirrors don't have the best search features. So you will have to just search for the username, in this case
Second, click on the username.
Third, scroll through until you find the picture you are looking for. Make note of the date so you know where in the timeline it will be. Hopefully, it isn't too far back otherwise you will be hitting next many times.
Fourth, when you find the picture, click on it, copy the URL and paste it into archive.is.
EDIT 2: Gramview is no longer available as of 6/25/19
EDIT 3 Web.Stagram is no longer available as of 6/25/19; Added Instadigg; Picbon has been renamed Picbob, Pictame is still up; Picsoro is now bebiram
EDIT 4 Removed hyperlinks from websites no longer active.
EDIT 5 Updated for April 2020
EDIT 6 and 7 Updated April 29 2020 with many more additional sites. Updated suggestions.