After you reclaim the red rock from the Reptites, you should go back to Melchior.
Go to Melchior
If you haven't already, use the northeast light pillar in the End of Time to go to 1000 A.D., Medina Village. Go outside and go west to Melchior's Hut. Go in and talk to him, and there will be a cutscene. Then go downstairs and there will be a cutscene.
Leave Melchior's hut, then go east to the village and use the Gate in the closet of the monsters' house. Then use the southeast light pillar to go to Leene Square. Go south to Lucca's house and talk to Taban. If he is not in the front room, go north and use the northeast stairs, and wait for Taban to appear. After he leaves the room, go south and talk to him to get a new item for Lucca.
Now go north to Leene Square and use the Gate near the Telepods to return to the End of Time. Use the northwest light pillar to go to 600 A.D. Make your way out of Truce Canyon, then go southwest, south across the bridge, and south to the Cursed Woods. Go into Frog's home in the bush at the north end of the woods, and talk to Frog to give him the Masamune. There will be a cutscene.
Take Frog to the End of Time and talk to Spekkio so Frog can learn magic. You can go back to Truce Canyon and use the Gate to get there. If Crono is level 19, you should battle Spekkio afterward to get the rewards from his Kilwala form.
After that, use the northwest light pillar to go back to 600 A.D. Exit Truce Canyon, go southwest, and go south across the bridge. You may wish to buy some Revives and Mid Tonics in Dorino before you proceed. Then go east from Dorino and Fiona's Villa to reach Magic Cave. Go in. There will be a cutscene.
After the cutscene, equip Frog with the Hero Medal to increase his critical hit rate.
Go east. Use magic on the rats, and use regular attacks on the bat.
You can avoid the second batch of monsters by walking to the right of them while the bats are on the left.
The dead soldier near the exit gives you a hint about fighting Jugglers.
Go north from the dead soldier to exit the cave, then go north and enter Magus's Lair.