Absolutely next to nothing is known about the Hellbent assassin Basilisk. When we are first introduce to him, Basilisk is already serving Seth and accompany by Agony. His first mission is to killed the leaderless Templar in a monastery in France, one he did with twisted pleasure. From there on Seth, send him and Agony to searched for Bloodlines.
Chloe Tran killed him by having him glance at a mirror.
As his name imply Basilisk's gaze is lethal, it never been shown what would happen if an undead or robot was to be gaze at but one can guess that they would be immune to it. He was not immune or able to control his powers, making him constantly wear shades.