This is not my solution, but since there were no guides when i came to look it up, I’m going to cut and paste a solution i found on gamefaqs.
Before you get to this boss, there will be another large worm you have to get past, dont confuse it for the boss. This one is good practice for the boss, simply shoot it in the tonsils riding toward or away from it, charging out of the way when it gets too close. Eventually it will allow you to ride up and hit B to finish.
Here is a strategy for The Stygian, credit goes to @FatalBipedalCow on gamefaqs. Just a note, you dont have to kill the smaller worms, just shoot and avoid until boss comes back each time:
“Ride next to Stygian, every now and then he will just ride along the surface giving you the opportunity to use your sword and knock the metal guard over his face off. Once you get it off he will start coming after you like the first worm you faced, so just shoot that little yellow thing on his mouth. After awhile he will start following you underground. He will pop up straight out of the ground trying to ht you, just turn tight and use boost. The other thing he will do is send smaller worms after you, about 3 or 4 at a time. They are quite fast so turn sharp and just keep shooting them. After a few rounds of doing this you will get the chance to run up to him and hit B for the kill.”