There is an unnecessary part to this sidequest which doesn't have any rewards so I am not going to cover it. In 600 AD go to Choras and then head to the Northwest, and you will see an island, land on it and enter the Giant's Claw. After heading through the Giant's Claw for a little while it should begin to look very familiar to you: it is the Tyrano Lair from 65,000,000 BC. Head through this familiar territory until you reach a section with buttons on the floor that cause holes to appear. You will need to deliberately fall down those holes to continue. Make your way to where Kino was held captive and save. There is now a path out of the back of Kino's cell so take it, but first equip fire- resistant armor etc. You will encounter the Rust Tyrano. Although he is tougher than the Black Tyrano, the same kind of strategy applies and he should be beaten without much fuss. After you have defeated him, head north to discover the Rainbow Shell. Unfortunately, the Rainbow Shell is too heavy for your party to carry so they will ask King Guardia if he will retrieve it for you. He agrees and decides to keep it in the castle as a family heirloom.

As well as any items/chests you missed when you first went through the Tyrano Lair you can also find the following new items from the Giant's Claw: Frenzy Band, Blue Rock, Zodiac Cape and Full Ether.

Put Marle in your party and head to the Guardia castle of 1000 AD. The Chancellor will approach you and tell you how the King was indirectly responsible for the death of Marle's mother. After you learn that the King is on trial, head up the stairs to the council room where Crono was tried earlier in the game. Marle will learn that the King is accused of selling precious family heirlooms such as the Rainbow Shell. Head down to the basement and fight your way through to the Rainbow Shell (you can find Elixir (x2), Hyper Ether (x2), Lapis (x2). At the extreme north of the basement you will find the Rainbow Shell.

Go back up to the room where the trial is taking place and talk to the guards. You will be denied entry but just as the Judge is pronouncing the King guilty, Marle will smash through the window and show a shard of the Rainbow Shell to the Judge and Jury. The Chancellor will reveal that he is Yakra XIII, a descendent of the Yakra defeated in 600 AD, and that he has come for revenge. This begins a boss fight with Yakra XIII. After you are victorious, Marle and the King will 'make up' and then Melchoir will come in and tell you that he is ready to make you some new weapons and equipment. Before you go and talk to Melchoir, you should head back to the room in which the trial was held and pick up the Yakra Key from off the floor. This can be used to unlock a previously locked chest in the castle which contained the real Chancellor.

Now, go back down to the Rainbow Shell in the basement and talk to Melchoir. He will offer you a choice between 3 Prism Helms and a Prism Dress. The Prism Dress is the superior piece of equipment, so I suggest you choose it. He will also make you the Prism Specs accessory and, providing you have done the sidequests in the order suggested, and have already gotten the Sun Stone, Melchoir will also make you Crono's ultimate weapon, the Rainbow!