Okay, here I'll give a short summary and explanation of why each weapon is Legendary, and mention some possible reasons for two weapons that aren't 100% confirmed.
Scourge of Svarog
Scourge of Svarog, this weapon became legendary by altering fate and divinity through the slaying of the deity Svarog. Much about this god and their role remains unknown.
Defiler of the Divine
Defiler of the Divine, this weapon became legendary due to two factors: by indirectly "killing" the Bishops by taking away their followers, and by killing all hope of these followers due to the loss of their faith.
Ruin of Nirah
Ruin of Nirah, this weapon became legendary due to the death of Nirah, a goddess. She had trusted the owner who carried this weapon, and he murdered her. Many more details about this Goddess are unknown.
Lamb's Slaughter
Lamb's Slaughter, this weapon became legendary due to the genocide committed against lambs using it, killing all hope.
Yngya's Torment
Yngya's Torment, this weapon became legendary because it was with this weapon that the Bishops killed Yngya, the Goddess of Winter, and the worshipped deity of the Lambs
Golden End
Golden End, this weapon's legendary status is not fully confirmed, but it could be assumed that one of the owner's parents was a descendant of the Gods of Gold who, like the Chosen Child, was born with Divinity, and became legendary after killing a God.
Fate of Plimbo the First
Fate of Plimbo the First, this weapon's legendary status is not fully confirmed, but there are discarded lines of dialogue from Plimbo that could have explained it. These lines would reveal that a very ancient ancestor of his was murdered by the weapon's owner, a bloodthirsty pirate, who killed Plimbo's ancestor to steal his treasure. This would indicate that the weapon had likely killed many individuals, making it legendary for killing all hope.