The first Gods walked in the early light among the green hills of Krypton in the beginning of time. The Gods and Goddesses of dawn reigned over a world in harmony and they fathered the lineages of man to worship them and live in peace, but harmony is not the way of life, even among the gods and out of the frozen blackness beyond the furthest reaches of the light came evil. All the people were afraid. Cythonna was lovely as the hoar-frost in the vale, but her heart was cold and her hate was deep. For all that was warm and light. She alone of all the gods could bear no children but birthed only roaring monsters of ice and rime.
And so she bought fear, cold, despair, and finally death into the world. her curse to the radiant warmth of the living. When first she came, she was a marvelous beauty of crystalline delight. And she spoke to the sun, great Rao, tender words of love and yearning seeking to make him hers. But Rao's brilliance lit even the blackest corners of Cythonna's heart and he saw that though she spoke of love she had no knowledge of it. She sought only his power to father her children, wild elementals she meant to send out into the wide, white world to corrupt the light and suborn the heat. Rao rejected her. So began the wars of ice and fire.
War of Fire & Ice
Cythonna was strong; the powers of the gods of dawn were new. And they had never fought in anger before. So across the space of many lifetimes darkness fell upon the face of Krypton. The days of dawn were over. In the end, the gods had mastery and they rendered judgement. They could not kill her but great Rao himself thrust her beyond the borders of existence through the iron gates of doom and they were sealed forever. She was said to wait in the eternal darkness of the frozen void and to gather unto herself the souls of the unforgiven dead but if the power of the gods ever weakens, she will return to finish what she started. Rao alone knows if she will succeed. The wars of ice and fire left scars that were never entirely healed.
Krypton's inhabitants became emotionless, branded for all time by the goddess's bitterness. Many of the young gods were dead. The rest, according to the legends, left Krypton for a distant realm where they might heal their hurts and recover. The faithful claimed that the gods would return to Krypton eventually and restore her. Apostates said that the gods had abandoned their former home and followers for all time. Skeptics said that there never were any gods, but an ancient race of protomen whose stories have come down to us. The origins of these tales are clouded in the mists of time. Their truth or falsity is beyond testing.
A few years after Lois Lane & Clark Kent/Superman got married she managed to escape to frozen void. Proclaiming that she had won the war of light and darkness, however she sensed a spark of life somewhere in the cosmos, a lifeforce tied directly to Rao himself. Angered by this, Cythonna decided to find and eliminate the last trace of Rao in this universe and took off flying into deep space. Five days later she appeared at the Daily Planet and after killing a woman Superman decided to confront her...and with a "casual backhand" managed to best Superman.
She claimed him as her mate and flew away saying that he was to meet her at "the roof of your world" in one hour. Lex Luthor then tried to meet with her and make a deal. He failed and had one of his men kill another. He drove away in great anger. Meanwhile, Superman was investigating Cythonna's claims. He found she was telling the truth. On his way to meet her, Luthor gave Superman some kryptonite to help him beat her.
Fall of a Goddess
With his plan set in motion Superman went on to challenge Cythonna. However his second fight with her didn't go exactly as planned. During the fight Superman was manhandled by Cythonna and barely managed to work up a small offense against her, and all the while as she was overwhelming him with her own might/powers fairly easily.
Only a combination of things would bring Cythonna to an end, when Superman would flee for his life to the sun. The powers of the sun, deriving from Rao, and being the universal opposite of Cythonna, was enough to weaken her down a level much closer to Superman's as he was also amped up to his full potential. Cythonna however still seemed to be slightly stronger, and then finally showing Superman her true monstrous form and continued physically controlling most of the fight, until a grenade of Kryptonite was used to further knock her back, only to finally be pulled in and enveloped by the sun. Where she remains to this day, trapped in a prison of eternal fire, watched over by Rao himself.
Cythonna is by far one of the most powerful beings in the DC Universe if not the most powerful. Even though her appearance was short lived, her presence still lives on Cythonna is an unmatched being who is omni-strength, omni-durability, omni-speed, omni-ice manipuation, omni-telepathy among various other all mighty powers. Various statements were given in the issue she appeared in about her unmatched strength.
Cythonna also possesses the ability to fly on her own will, survive in space unaided, and being so fast that she seemed to be untouchable by Superman. With great power, also causes arrogance to the point where she can be outsmarted.
On Superman's first encounter with her, a single backhand, almost knocked him out. He was unable to rise to his feet quickly enough to chase her. A surprised spectator shouted "good Lord", at the display of Cythonna incapacitating the Hero most thought would be able to oppose her, with such ease. He would later express to Lois, "I'm scared myself Lois, her blow was easily as strong as any I took from the three super criminals I was once forced to execute, and this was a backhand, a casual one"
While flying with Lois in his arms after his first encounter with Cythonna, Lois exclaimed, "I've never seen you so worried Clark, are you sure she didn't hurt you". Superman responded with, "She demonstrated a complete contempt for life, a sensitivity bordering on the telepathic, and a strength beyond anything I've ever encountered".
Given Superman's statement this would make Cythonna more powerful than beings the likes of Doomsday, Mongul, and Darkseid in the DCU. Superman in his fights against these previously mentioned beings was able to mount up an offense against them and severely damage them or kill them in order to beat them. However When fighting Cythonna, Superman couldn't get a good offense going against her, and even while he did manage to hit her a few times, he caused no virtual damage to the Goddess and quickly found himself being tossed around by her. Seems for Cythonna besting Superman was a mere task.
This is consistent to her showings, because Rao himself could not physically overpower Cythonna, showing that she dwarves his strength. As a major God of the Kryptonian's, Rao is considered as one of the most powerful beings in the DC Universe. As he is stated to have created the heavens and such in Kryptonian Religion/Mythology.
During a one sided fight when Cythonna nearly killed Superman using a bit of her telepathic abilities, some of her ice powers, and more than anything, the unmatched strength of her bare hands, she stated, "now child of light despair, even the God's could not destroy me", again validating that multiple major deities were only able to vanish her for a time, and not able to over power her enough to kill her.