After becoming a Demon Daki grew strong enough to kill and eat seven Pillars and gained the attention of Muzan Kibutsuji who allowed them to join the Twelve Demon Moons. She later dies after being beheaded by Zenitsu Agatsuma and Inosuke Hashibira.
Daki has one of the saddest backstories in the entire series. She never even wanted to turn into a demon but was forced into becoming one after being burnt alive at the hands of a pushy client, leading to a desperate Gyutaro accepting the notion of becoming a demon so that her sister could remain alive.
Muzan himself never thought highly of Daki and didn't reciprocate her devotion whatsoever, only ever talking to her to sweetly manipulate her into defeating Demon Slayers on his behalf.
As a member of the Upper-Rank Six, Daki was extremely powerful. She was much more powerful than the regular demons. Her physical abilities were on a completely different level in comparison to some demons that Tanjiro and co. had faced. Daki was immune to decapitation when her brother was attached to her core.
At some point, Daki fought, killed and ate seven Hashira. Two days before Tanjiro Kamado and company infiltrated the Entertainment District, Daki was confronted by Omitsu, the manager of the Kyogoku House, over her mistreatment of the staff.
Nezuko is at least stronger than Daki, meaning that if Muzan could bring her back under his control, she would certainly qualify for the most prestigious title a demon can hold: a member of the Twelve Kizuki. Thanks to Nezuko's remarkable strength, she would have to be an Upper-Moon.
Even 400 years later, Muzan's fear of Yoriichi remained fully intact, as simply laying eyes on Tanjiro's hanafuda earrings caused him to recall their clash.
Yoriichi was incredibly proficient in his Sun Breathing, being able to take down demons effortlessly and even overwhelm the Demon King and strongest Upper Rank.
Before he is able to regenerate fully, Tamayo appears and uses her Blood Demon Art to keep him in place, while using a drug that can turn him into human. Using this opportunity, Gyomei Himejima appears and destroys Muzan's head.
The Samurai not only insulted Gyutaro in front of Daki but also made fun of his malnourished body and disease. As Daki was unable to tolerate the insult of her brother, she took off her Kanzashi and stabbed the left eye of the Samurai.
Daki/Ume was offered the chance to go to heaven presumably because she didn't choose to become a demon, and she was only 13 when she turned.
Nezuko setting Tengen on fire. By the end of the battle, Gyutaro's poison has spread throughout Tengen's body resulting in his inability to speak. As he lays dying from the poison, Nezuko Kamado intervenes and uses her her Blood Demon Art to burn the poison out of his system, allowing him to rejoice with his wives.
The last member, Upper Moon Four Nakime, ends up being killed by Muzan Kibutsuji himself to stop the Dimensional Infinity Fortress from being controlled by his enemies.
Fortunately, Zenitsu was able to single handedly beat the Upper Moon 6. Not only did he defeat the demon, he also created a seventh form called the Flaming Thunder God. These are the demons who have been given the title of Upper Moon 6 in Demon Slayer.
Curse of Kibutsuji
This curse besotted any who partake of Muzan's blood must be careful. The curse prevents Muzan's name from being spoken aloud, and any who do will meet a horrible demise. One demon, Susamaru, faced this reality when battling Tamayo.
The explosion, which was enhanced by spike traps, manages to injure Muzan. Before he is able to regenerate fully, Tamayo appears and uses her Blood Demon Art to keep him in place, while using a drug that can turn him into human. Using this opportunity, Gyomei Himejima appears and destroys Muzan's head.
Don't go! DON'T LEAVE ME HERE! Muzan speaks his final words as he loses control over Tanjiro.
Akaza was also one of Muzan's favorite demons out of all his subordinates. The reason behind this is Akaza's extreme loyalty to his master. The Upper Rank Three demon was always sent away on special missions, something the Upper Rank 1 and 2 were often denied of.
Tanjiro certainly did a lot of good with his Water Breathing techniques, but his ability to use Sun Breathing both gives him an edge in battle and allows him to stand out among the incredibly powerful Hashira he fights alongside.
However, Tanjiro is not a descendant of Yoriichi Tsukiguni. Tanjiro is the descendant of someone who knew Yoriichi personally and was a good friend of his as well. Sumiyoshi was rescued by Yoriichi when a demon threatened his life. Since then Yoriichi often met him and they became close acquaintances.
As a result, Tengen Uzui has to deal with the moniker of being the least powerful Hashira around. Of course, that's not the worst thing in the world, as all Hashira are strong. He's still incredibly powerful and can give any demon a run for their money.
She was ranked in 3rd place in the first Demon Slayer character popularity poll with 3,319 votes. IGN regarded Nezuko as one of the series's most popular characters and noted how her design elaborates the way she sees humans as good people as a result of hypnosis.
Akaza's rank is far superior to that of the Gyutaro and Daki, and an upper-rank demon is more powerful than the demons with a lower rank. That said, this fight will be two against one. In order to mark his victory, Akaza has to defeat both the sibling demons which can be a bit hard.