If you want to view private Instagram profiles, there are a couple of things you NEED to know:
Most importantly, gaining unauthorized access to someone else's private data is actually illegal. Not sure what the outcome would be if you go to court, but is it really worth it?
Spending your time learning how to hack a private Instagram profile sounds kinda lame.. Don't you have better things to do with your time?
If you really are desperate to hack someone's Instagram account, check out videos on YouTube like this one below:
I can't guarantee that it will work, and I'm sure Instagram's security upgrades on a regular basis, so as soon as this hack starts getting popular, they should clamp down on it.
Also, it asks you to download some sort of software.
Personally, I don't trust software made by hackers.. Who's to say they aren't going to hack you too?