Snoopreport is an Instagram activity tracker that allows you to monitor the actions of users with a public profile. I use this tool to keep up with the interests of my friends and fav celebrities. It is quite handy because you get weekly reports on which hashtags and posts users like, their thematic interests, as well as new followings and unfollowings.
The big advantage is that there is no app to install, this is an online tool that you can use on any device. You don't need to have your own Instagram profile to follow someone's activity. After Insta removed the ability to monitor friends' activity through the following tab, this tool is the most reliable and cheap solution.
However, it is impossible to track private Instagram profiles.
SnoopReport