Cocytus Star is a demon in the series.
Cocytus, also known as Kokytos ("lamentation"), is the river of wailing in the underworld in Greek mythology. Cocytus flows into the river Acheron, and on the other side lies Hades, the underworld. There are five rivers encircling Hades: the Styx, Phlegethon, Lethe, Acheron and Cocytus.
In Inferno, the first cantica of Dante's Divine Comedy, Cocytus is the ninth and lowest circle of The Underworld. It is referred to as a frozen lake rather than a river, although it originates from the same source as the other infernal rivers, the tears of a statue called The Old Man of Crete which represents the sins of humanity. Dante describes Cocytus as being the home of traitors and those who committed acts of complex fraud. Depending on the form of their treachery, inhabitants are buried in ice to a varying degree, anywhere from neck-high to completely submerged.
Cocytus also makes an appearance in John Milton's epic poem Paradise Lost.
Shin Megami Tensei V
"A star of ice created by Lucifer.
In Dante's "Divine Comedy", the former angel is shown buried in the frozen Cocytus, deep within the darkest depths of the underworld. Those who are hit with this falling star are said to be frozen even long after death."
The Cocytus Star is summoned by Lucifer during the battle.
The Cocytus and the Brimstone stars have unique properties, as they have weaknesses parallel to Fire and Ice, but will grant Lucifer a weakness of the opposite type. In the case that both stars are present, Lucifer will gain both weaknesses. When the stars are destroyed, Lucifer's respective weakness will disappear along with them. However, if the stars aren't destroyed by the end of the next player turn, Lucifer will cast a severe piercing attack to 1 target. It is very easy for them to suffer an instant death. As such, the player's strategy will need to be planned out carefully, budgeting some turns to damage Lucifer while still having enough turns to destroy the star. If not, simply destroying the star and ignoring the opening Lucifer gives himself is enough.