Most of this info comes from Sacred Texts.
Myths About Horus
The Birth and Flight of Horus
This tale, found in the Coffin Texts, is a combination of two stories. The first is the birth of Horus, and the second is a very old and fragmented myth that the sun burst out of an egg laid by a primeval being or goose floating on the primordial waters before creation. The Birth and Flight of Horus begins just after Osiris's death. The tone is much more serious than that of the Delta Cycle or the Great Quarrel.
The world was being terrorized by Set. Isis dreamed that she would have a son who would avenge her husband's death and asked Atum if this son would be allowed a seat on the sun boat. However, just before the birth, Isis realized that she would be giving birth to a Falcon, not a child. Upon the birth, Atum saluted Horus and told him that he would give him his name after Horus flew to the horizon. While the company was discussing other matters, such as Horus's seat on the boat, Horus flew up on his own, higher than even the "old" gods who inhabited the constellations. Horus proclaimed to the gods below that he would, indeed, avenge his father's death.
This myth, as mentioned before, combines two others together. According to some sources, there were actually two gods named Horus. The first, the original Falcon, flew up at the beginning of time upon his birth. The second, son of Isis, was forced to grow up in secret for fear of Set, as described in the Delta Cycle myth. The myth of the Birth and Flight of Horus brings these two gods into one.
The Contendings of Horus and Set
This is part of the Delta Cycle Myth.
After 80 years of a tribunal of the Ennead over who should rule now Osiris is dead (Horus his son or Set his brother) a decision must be made. Isis tricks Seth into judging for Horus but he persuades the gods to allow them to dual. Isis tries to help Horus again but hurts him instead and he cuts her head off. Seth then plucks out Horus eyes and buries them. Hathor heals his eyes with gazelle's milk. Then Seth violates Horus but Isis and Horus together fool Seth into eating some of Horus semen on a lettuce. Seth tells the tribunal he has had Horus, but Horus proves his seed is inside Seth not vice versa. They race in boats then fight again, then write to Osirtis, then fight again. Ths time Horus beats Seth and he is crowned with the white crown and Seth goes with Pre-Harakhti to make thunder in the sky.
From the papyrus found by Chester Beatty originally belonging to Qenherjopshef, born in year 16 of the reign of Rameses II (19th Dynasty, 1279-1212 BC). Before being deposited in the tomb it was found in it passed down the descendants of Qenherjopshef. The fifth, a carpenter called Maanajtef, cut parts of it to use it in his private correspondence. It was found between a pyramid and the vault of a tomb, possibly placed there to protect it during the period of instability of end of the 20th Dynasty.
THE LEGEND OF THE GOD NEB-ER-TCHER, AND THE HISTORY OF CREATION
In this text from 311 BCE the embraces of Keb (earth god) caused Nut (sky goddess) to bring forth five gods at a birth; Osiris, Horus, Set, Isis, and Nephthys. Osiris and Isis married before their birth, and Isis brought forth a son called Horus; Set and Nephthys also married before their birth.
THE LEGEND OF HERU-BEHUTET AND THE WINGED DISK
The text of this legend is cut in hieroglyphics on the walls of the temple of Edfu in Upper Egypt, and certain portions of it are illustrated by large bas-reliefs. Both text and reliefs were published by Professor Naville in his volume entitled Mythe d'Horus, fol, plates 12-19, Geneva, 1870. The legend, in the form in which it is here given, dates from the Ptolemaic Period.
From Nubia Ra-Harmakhis sailed down the river to Edfu, where Heru-Behutet entered his boat, and told him that his foes were conspiring against him. Ra-Harmakhis addressed Heru-Behutet as his son, and commanded him to set out without delay and slay the wicked rebels. Then Heru-Behutet took the form of a great winged Disk, and at once flew up into the sky, where he took the place of Ra, the old Sun-god. Looking down from the height of heaven he was able to discover the whereabouts of the rebels, and he pursued them in the form of a winged disk. Then he attacked them with such violence that they became dazed, and could neither see where they were going, nor hear, the result of this being that they slew each other, and in a very short time they were all dead. Thoth, seeing this, told Ra that because Horus had appeared as a great winged disk he must be called "Heru-Behutet," and by this name Horus was known ever after at Edfu.
In gladness of heart Ra proposed a sail on the Nile, but as soon as his enemies heard that he was coming, they changed themselves into crocodiles and hippopotami, so that they might be able to wreck his boat and devour him. As the boat of the god approached them they opened their jaws to crush it, but Horus and his followers came quickly on the scene, and defeated their purpose. Horus then associated with himself the goddesses Uatchet and Nekhebet, who were in the form of serpents, and, taking his place as the winged Disk on the front of the Boat of Ra, destroyed all the enemies of Ra wheresoever he found them.
After this Set shows up with an army and Horus defeats him too. Then Horus son of Isis shows up and cuts of Seth's head and Isis appoints Horus of Behutet the protecting deity of her son Horus. There's a lot more fighting then when Horus returns in triumph to Edfu, Ra orders that an image of the winged Disk should be placed in each of his sanctuaries, and that in every place wherein a winged Disk was set, that sanctuary should be a sanctuary of Horus of Behutet. The winged disks which are seen above the doorways of the temples still standing in Egypt show that the command of Ra, was faithfully carried out by the priests.
THE BIRTH OF HORUS, SON OF ISIS AND OSIRIS
From a stele on which the greater part of the text consists of a hymn to Osiris, which was probably composed under the 18th Dynasty. The last paragraph of the text contains an allusion to Isis, the sister and wife of Osiris, and mentions the legend of the birth of Horus, which even under the 18th Dynasty was very ancient.
The Pyramid Texts state that the body of Osiris was hurled to the ground by Set at a place called Netat, which seems to have been near Abydos (Pepi I., line 475; Pepi II., line 1263.) The news of the death of Osiris was brought to Isis, and she at once set out to find his body. All legends agree in saying that she took the form of a bird, and that she flew about unceasingly, going hither and thither, and uttering wailing cries of grief. At length she found the body, and with a piercing cry she alighted on the ground. The Pyramid Texts say that Nephthys was with her that "Isis came, Nephthys came, the one on the right side, the other on the left side, one in the form of a Hat bird, the other in the form of a Tchert bird, and they found Osiris thrown on the ground in Netat by his brother Set." The late form of the legend goes on to say that Isis fanned the body with her feathers, and produced air, and that at length she caused the inert members of Osiris to move, and drew from him his essence, wherefrom she produced her child Horus.
Pyramid Text, Teta, l. 276. - Thy sister Isis cometh to thee rejoicing in her love for thee. Thou hast union with her, thy seed entereth her. She conceiveth in the form of the star Septet (Sothis). Horus-Sept issueth from thee in the form of Horus, dweller in the star Septet. Thou makest a spirit to be in him in his name 'Spirit dwelling in the god Tchentru.' He avengeth thee in his name of 'Horus, the son who avenged his father.' Hail, Osiris, Keb hath brought to thee Horus, he hath avenged thee, he hath brought to thee the hearts of the gods, Horus hath given thee his Eye, thou hast taken possession of the Urert Crown thereby at the head of the gods. Horus hath presented to thee thy members, he hath collected them completely, there is no disorder in thee. Thoth hath seized thy enemy and hath slain him and those who were with him."