Surviving Village - Market
Take that, Dalton. After destroying the Blackbird you’ll wind up back near the Surviving Village. Have a look around, if you wish, and check out the Nu and his new wares. You may notice a weapon no one in the party can use. Interesting.
You can’t use the Epoch right now, so after saving and healing you'll want to head to the North Cape, a small location on the northern end of the island. You may be facing a battle in a few moments, and the nature of the battle changes depending on whether or not you have Frog in the party. Equip magic resistant armor if you decide you want a fight.
Check the glittering item resting on the Cape. A lengthy cut scene that explains a lot follows. After that, you'll need to make a very important choice.
Magus
Once the all-powerful Magus is done telling his story, he’ll challenge the party to a fight. Unlike the last one, you can choose to turn him down - and if you do, Magus joins the party. Magus is a pretty rocking party member, and though he’s incapable of performing Double and Triple Techs with his teammates under most circumstances - presumably because he’s an antisocial jerk - he’ll prove useful in virtually every battle from this point on.
If you decide to fight Magus, well... time to rumble. The battle changes depending on who’s in your party; if it’s anybody but Frog, you’ll have three party members. If Frog’s around, though, he’ll take on Magus solo. If you win this fight you may see a different ending for Frog once the game's over, depending on the route you take.
Magus with Frog
HP: 6,666
If you decide to battle Magus with just Frog you’ll be facing a tricky battle. Having lost much of his magic, Magus nevertheless retains his second tier elemental spells (Lightning II, Ice II, Fire II), and he likes smacking Frog around with his scythe. Fortunately, Frog will be a fair bit stronger this time around, and can handle Magus alone.
Keep Frog's health high with items and spells and use your strongest Techs to whittle away at Magus’s copious amounts of HP. He doesn’t have his elemental absorption abilities this time, so you can use whatever attacks you like from the get-go. You can further tilt things in Frog's favor by equipping him with armor that deadens elemental attacks. The Rage Band is a good accessory to add, as it allows Frog to counterattack Magus's scythe strikes, though if you decide to use the Masamune you'll want the Hero's Badge for a higher crit rate. Your call.
Magus without Frog
HP: 6,666
Charm: Megaelixir
If you don't have Frog in your party then this battle’s an absolute breeze. Magus has lots of HP, but he can’t dish out enough damage to be a serious threat unless you completely neglect your health. Use your strongest Dual Techs to rip him to pieces.
(This battle seems rather variable. In some cases Magus will unleash his magic rather quickly. In others he may plink weakly at you with physical attacks until you drain his HP. Hopefully you get a satisfying brawl.)
Kill Magus and he’ll leave the Amulet behind for you to grab. Recruit him and he’ll have it equipped. Either way, head back to the Epoch and climb in. A cut scene follows, and you now have a new fixture in the sky: The Black Omen. This is essentially Chrono Trigger’s final dungeon, though you don’t need to enter it to beat the game. If you're playing the DS or PC versions of Chrono Trigger this will also unlock the Lost Sanctum, a dungeon that was not part of the original game.
The Rest of the Game
You’ve now arrived at a crossroads of sorts. With a winged Epoch you can fly to, and explore, every time period in the game. You can even use it to bypass the first phase of the Lavos battle, though if you’re not strong enough to fight Lavos’s shell you won’t have a hope of beating its core components. Everything besides beating Lavos, in short, is now optional. You can do as you please… and that even includes not resurrecting Crono.