THE SOLUTION
There are a few different ways you can defeat Haderax the Invincible. The easiest way is to have someone at a higher level join your game and have them kill Haderax for you. In Normal Vault Hunter Mode, he is level 38-40 depending on what level you finished the DLC.
If you are doing this solo, you can get yourself over leveled, and go back to Normal Vault Hunter Mode and take him down or you if you want the challenge, I'll have the steps below on how you can kill him.
For a legit kill
You're going to want the retainer and toothpick set that can be farmed off the sand worms in The Burrows. This gives you a massive speed boost while in The Writhing Deep, which is where you fight Haderax. You'll notice that when you fight haderax, he will heal whenever he goes underground. To stop him from healing, you need to have him slagged. If he is slagged while tunneling underground, he will not heal.
Now for damaging him. He is weak to fire damage. But just hitting him anywhere will not do enough damage to kill him effectively. On top of his head, there is a large yellow-ish area that is his crit spot. If you shoot that enough, he will slump forward and be stunned for a short period of time. Using a fire weapon and a bee shield will melt his health bar.
Credit to RuneSlayer4421