I upgraded both my iPad mini w/Retina and my iPhone 4s to iOS 8.4 . My iPad mini is working fine. I had a problem with my iPhone, however. I was out and was attempting to login to a public wifi. It began to fall into a reboot loop. Restart, restart, restart. As it turned out, I am running a VPN app called Betternet. As soon as my phone attempted to connect to wifi with the VPN option in Settings toggled to the "ON" position, my phone would crash. So, immediately after booting up and entering my lock screen password I saw my home screen. I clicked on Settings right away, and tried to toggle VPN to "OFF". Phone crashed again before I could switch it. The next time on reboot, I deleted the Betternet app before my phone could even try to initialize a wifi connection. With the app gone, there was no longer a VPN option in Settings. My phone has now been ON for 20 hours with no more crashing or problems. My problem appears to have been an app vs. iOS version incompatibility. Perhaps this will solve your issue.
That's it. I hope that helps. Oh, by the way, I found similar advice on the Betternet user forums page of their website suggesting the same solution for Betternet users after I had removed the app.