Cyrus Sidequest - Starts in Choras Village 600 AD
When speaking to the Old Man in The End of Time, the fifth side quest that he tells you about involves Frog's storyline and takes place in 600 AD / 1000 AD. The quest text is, "There's the ghost of a lofty knight, slain by Magus in the Middle Ages, who haunts the present."
To get started with this quest head to Chorus Village in 600 AD, it's just south of the Northern Ruins on my map above. Speak to the man sitting at the table in the Cafe and he'll tell you that he needs tools in order to fix the Northern Ruins. Toma in the cafe will give you Toma's Pop which is part of the Rainbow Shell Sidequest.
Once you've spoken to the man in the Cafe and are told about the tools, board the Epoch and travel to Choras in 1000 AD. In the Inn there'll be a man who you can talk to who will lend you some tools. He tells you to speak to his wife in a nearby Residence, do so and she'll give you the tools. Back to Choras in 600 AD.
Speak with the man in the Cafe now that you have the tools and he'll return to his Residence nearby, the same one we got the tools from in 1000 AD. Go there, speak with him again and he'll tell you that he's traveling to the Northern Ruins, which are north of the town of Choras. Go to the Northern Ruins now which is a dungeon that we'll need to clear out for this NPC.
The enemies in Northern Ruins are all pretty easy, just bring Magus with you or Lucca and use Fire 2 which will likely one shot every enemy in this place. After you the rooms on both the right and left sides of the staircases return to the Residence in Choras 1000 AD and talk to the man again. He'll tell you that for 2000G he'll repair the Northern Ruins, accept his offer.
Switch your party up and make sure that Frog is a member before returning to the Northern Ruins. Take the left staircase and venture through the dungeon until you reach the grave of Cyrus. A scene will commence where Frog speaks with Cyrus and gets the upgraded Masamune. Exit the Northern Ruins again, return to the Residence in Choras and pay the repairman more gold to repair even more of the Northern Ruins.
Return to the Northern Ruins in 600 AD and this time take the staircase on the right hand side. All of the holes in the floor will be repaired and you'll be able to access all of the Sealed Chests in this dungeon. If you only examine the Sealed Chests here and don't take their contents - you'll power up the chests in the future which'll means you'll get better rewards!
600 AD Northern Ruins Sealed Chest Loot: Nova Armor, Kali Blade and Siren
1000 AD Hero's Grave Sealed Chest Loot: Moon Armor, Shiva Edge and Valkerye
Inspect all three chests then return to the Epoch and travel to 1000 AD. The Northern Ruins is renamed Hero's Grave, enter it and this time go around the dungeon and pick up each of the three Sealed Chests to get the powered up loot. When you're done, return to the Northern Ruins in 600 AD and loot all of the chests yet again for the lesser items.