For all of those wondering- i have (thus far) Found two different ways you can beat Basilisco.

The first: is to destroy all of the weak-points- such as the wings- until you do enough damage to make it run away.

The second: Is to do catastrophic damage to the head and body segments near the head- and you have to do it rapidly to prevent Basilisco from running away. (So-far i have only been able to do it with modded weapons) Destroy them and you should see a big cloud of red mist and hear a horrific death-screech. The remaining pieces will fall to the ground.

If anyone has found any other ways to defeat Basilisco, or tips on how to survive and fight it- please post them below.

-Good luck!