You now absolutely be able to Jailbreak iOS 8.4 successfully in both Window and Mac System yet. With new TaiG 2.2, iOS 8.4, iOS 8.3, iOS 8.2 and iOS 8.1.3 can be jailbroken completely – Jailbreak iOS 8.0.x -> 8.4.
TaiG 2.2 supports iPhone 6, iPhone 6 plus, iPhone 5s, iPhone 5c, iPhone 5, iPhone 4s, iPad Air 2 and 1, iPad 4 3 2 1, iPad mini 3 2 1 and iPod touch 5. Just a few click, mac users can jailbreak All devices quickly.
Jailbreak iOS 8.4 in Window 10
You should download the newest version of TaiG. Go here to check and get it: http://www.taig.com/en/
Step 1: Turn Off Passcode by Settings > Touch ID & Passcode.
Step 2: Turn Off Find my iPhone by Settings > iCloud > Find my iPhone.
Step 3: Run TaiG and connect iPhone to PC through USB, unstick 3K Assistant.
Step 4: Click on Start to begin doing Jailbreak iOS 8.4
Jailbreak iOS 8.4 in Mac OS X
TaiG 2.2 now has version for Window only. But you can absolutely run and Jailbreak iOS 8.4 in Mac OS X in a Windows running inside Mac OS X through VMWare fusion. Look at: Install OS X Yosemite/El Capitan on VMware Workstation 11 in Windows.
Newest update on 4th Aug 2015:
There has been TaiG V1.0 for Mac that supports to jailbreak iOS 8.1.3, 8.2, 8.3, 8.4 in OS X on Macbooks.
If you get it failed or encounter any troubles and errors during the jailbreaking processes, look at – Solve common problem, error, frozen stuck in Jailbreaking.