There is no way to view private albums on Facebook without getting a friend request.
That is the truth.
There used to be security flaws that would allow you unauthorised access to private albums and profiles, but they have been closed.
There are also Facebook "hackers" like this guy who says he can help you hack any Facebook album:
Sadly this stuff is all fake, and made up just to get YouTube views.
If you really want to access someone's private album, you need to do one thing:
Set up a decoy account and send them a friend request. Here's the full method of how you do that: http://internet.blurtit.com/3955992/how-to-view-private-facebook-pictures