Step 1: Grab the latest TaiG Jailbreak version from here: Download TaiG 2.1.2 For iOS 8.3 Jailbreak With Support For Cydia Substrate. (Update: v2.1.3 is available now, download that instead from here.)
Step 2: On the iOS device in question make sure that Find My iPhone and Passcode/Touch ID are turned OFF. To achieve this, head to Settings > Touch ID & Passcode > Enter your current Passcode and then select Turn Passcode Off. This will prompt for the current Passcode once more to verify. Similarly, to turn Find My iPhone off head to Settings > iCloud > Find My iPhone and select the relevant option to turn that particular location tracking service off.
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Step 3: Connect the iOS device running iOS 8.1.3 – 8.3 to a Windows computer. Open the downloaded TaiG Jailbreak tool.
Step 4: If the Apple device can’t be discovered by the jailbreak tool, it will present a window that clearly shows “Can’t find Apple device“. However, if everything is detected correctly a different window will be presented showing the details pertaining to the device and the DEBs that will be installed.
Step 5: We recommend keeping the Cydia option checked but unchecking the 3K Assistant option. Click Start to proceed with the jailbreak procedure.