They Exist. Ultra Rare Lost Song drops with potentially +300 more Attack power than average.
The list is as follows:
1Hand Sword – Blazing Sword
1236-1421
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Dagger – Fragarach
942-1118
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Rapier – Glaring Light
1031-1223
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Mace – Caduceus
1105-1294
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2Hand Sword – Durandal
1735-1952
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Knuckle – Iron Fist Oguma
980-1148
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Katana – Demon Blade Muramasa
1425-1646
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Spear – Brave Song
1337-1530
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Axe – Lang
1819-2060
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Bow – Silvan Bow
884-1069
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These are the Strongest Weapons in the game. Ideally you would want them with a bit of Elemental Attack as well. That way you can put them on the respective character that specializes in that element and you can get Maximum Damage.
Due to the extremely low probability of these weapons dropping, its okay if you think of some of them as a Myth.
Here’s the list again in picture form (For sending to people over PSN):