I was kind of surprised how easy it actually was to view private Instagram accounts. Until recently, you could just hack the private Instagram account by using a technique called a cross-site request forgery (CSRF) attack.
However, this "glitch" or "loophole" in Instagram's security settings seems to have been fixed.
So now he only way is to follow these steps:
1. Find the person on Facebook or Twitter:
This may take some time, but if you're a dedicated hacker, then you will go through with this!
3. Use the friend's photos and bio to make an Instagram account
You need to make it look genuine, so it's a good idea to follow as many mutual people as possible. Again, time consuming - but this is a really good tactic because it's likely they won't notice your account is fake for a very long time, and not only will you be able to spy on the private account... But you will also be able to cause some trouble through commenting on Instagram :)
4. Obviously, as mentioned above - the final step would be to add the private profile on Instagram, and wait for them to take the bait.
I have done this 4 times so far, and it has worked each time!
In one hack, I managed to make the private profile think a guy in our class wanted to go out with her when he didn't even know who she was!!!
