A jailbreak has been released for iOS 8.3 by the TaiG team. This jailbreak supports iOS 8.1.3 through iOS 8.3 and is Windows only.
The tool, which is dubbed TaiG 2.0. This release is quite interesting, since it was thought that the Pangu team would be the one to release a jailbreak for iOS 8.3 and TaiG would focus on iOS 9. That, obviously, is no longer the case.
Keep in mind that lots of things still need to be updated for iOS 8.3, including Cydia Substrate. Thus, support is limited with regard to jailbreak tweaks and apps.
Step 1: Download and extract TaiG 2.0
Step 2: Disable Find My iPhone and Passcode lock on your device
Step 3: Connect your device to your computer
Step 4: Run the TaiG 2.0 tool and it should detect your device
Step 5: Uncheck the 3K assistant, but keep Cydia checked
Step 6: Click Start
Step 7: Wait until the jailbreak completes. If you see storage full errors, just ignore those
Step 8: Once the jailbreak completes, find the Cydia app on your Home screen and launch it