The TaiG jailbreak tool has now been update to 1.2 and available with iOS 8.1.2 support. The TaiG jailbreak tool works on iOS 8 through iOS 8.1.2 and is available down below.
Before jailbreaking your device I strongly recommend making sure that the box next to the 3K Assistant feature is unchecked.
Everything is pretty much self explanatory from here. So now you can download TaiG for iOS 8 through 8.1.2 below.
Download TaiG 1.2 (English) from here.