The Chaos Cyclops appears in the latter floors of the Monad Depths within Tartarus. It will begin appearing from the 6th floor onward, once the shadow types of the block begin appearing in mixed groups. Its appearance so quite rare.
In The Answer it will appear in Empyrean as Red Shadow with 2 different Cyclops
Chaos Cyclops appears in the 6th and 7th Paradise of Heaven within the Midnight Channel. It will alternate between physical attacks and Electricity skills. While not being set as a weak point, it will take three times as much damage from Fire attacks. After being defeated, it may drop a Blade Thorn. Selling 8 Blade Thorns will unlock the Chain Glove claws for Teddie in the shop.
In Golden, it appears in Paradise 5 through 9 but its appearance so quite rare.. It may drop Sphalerite for trade at Shiroku Pub.