After you reclaim the red rock from the Reptites, you should go back to Melchior.
An Ending Available Now
Use the bucket (or the Telepod in a New Game +) if you can beat Lavos now for ending "People of the Times"
Go to Melchior
Now take the pillar to 1000 A.D., Medina Village. Go to Melchior's Hut and talk to him to repair the Masamune. Go downstairs and watch.
While you're in 1000 A.D., go visit Taban, he has a new item for Lucca.
Now go to 600 A.D., to the Cursed Woods, and give Frog the Masamune. He'll join.
**IMPORTANT** take Frog to the END OF TIME, so he can learn magic from Spekkio. When I went, Crono was at level 17, so I had him and Frog and Lucca fight Spekkio, and, though Spekkio's magic hit harder, I still won. Not hard, and it takes care of the gifts you get from his Kilwala form.
Use the bucket (or telepod in New Game +) if you can beat Lavos now for ending "The Oath"
When that's all done with, go back to 600 A.D., to the Magic Cave, east of Fiona's Villa.
When Frog gets the Masamune equipped, equip him with the Hero Medal as well, for a higher critical hit rate.
Use magic on the rats, and regular attacks on the bat.
You can avoid the second batch of monsters by walking to the right of them while the bats are at the left.
The dead soldier gives you a hint about fighting Jugglers.
Now go into Magus's Lair.