To Jailbreak iOS 8.4 all you have to do is:
- Always back up your data
- Disable Touch ID, pass code, and find my iPhone
- Turn on Airplane Mode
- Download TaiG Jailbreak V2.2.0
- Connect your iDevice and run the jailbreak tool
- Uncheck the bottom checkbox and hit the green button
- Wait for the process to end
- One the green face appears, your device well reboot
- Turn off Airplane Mode and then open Cydia
- Done !!
That's it, you are now running the Untethered Jailbreak on your iOS 8.4 devices, and can enjoy even more customizations and tweaks. Unfortunately this Jailbreak is only compatible with Windows for now, while a Mac version is expected to be released later on.