The Bloodshot Eye is a monster which will spawn during a Blood Moon. It has the Demon Eye AI and is a source of Black Lenses and Bloodshot Lenses. Both are required to summon the boss Cataryst.
Unlike Demon Eyes however, its rate of dropping Black Lens is much higher (3% instead of 0.67%). This means that farming Bloodshot Eyes during the Blood Moon in which they spawn is a more efficient way of acquiring Black Lens for any recipes requiring them.
Bloodshot Lens (35%)
Black Lens (3%)