(adsbygoogle = window.adsbygoogle || []).push({}); Right now my iPhone 5s is running 8.1.2 jailbroken with the jailbreak tool from TaiG. The question is: How do I go about updating to 8.3 and then jailbreaking it again?

Resote to 8.3 Via iTunes the JB using the new JB tool

You mention "restore" and not update. I am kinda confused. Are you saying that I back up my phone and then restore it via iTunes on 8.3.

First things first. Back up your iPhone (so you have all your stuff, photos/music/apps/notes etc.

Update to 8.3 firmware. Once that's complete, click restore and choose the back up (will be the most up to date one).
Now jailbreak.