The Dark Eagle Shadows are first encountered in the later floors of the Arqa Block, from Floor 48 on up. They may drop Turqoise gems upon defeat. They will later be found in the second and third sections of Antenora within the Abyss of Time.
Dark Eagles are common enemies on Paradise 2 of Heaven. They may drop Jet Black Steel upon being defeated, and selling 4 of these to Daidara will unlock the Demon Shield in the shop inventory for Kanji.
In Golden, it appears in Paradise 2 to 4 of Heaven. It may drop Rose Quartz for trade at Shiroku Pub.