Chrono Trigger/Unnatural Selection?

'''Unnatural Selection? (65M B.C. second time)'''

You'll have Ayla in your party no matter what for this chapter, although you can pick the third member if you wish. You can take her to the end of time to meet Spekkio if you want, but she won't be able to learn magic since she predates its existence on the planet. Stop by the trader hut to pick up the best weapons and armor available if you haven't already, and fly your dactyl into the Tyrano Lair to move on. Since this is your first time when you're able to fly, I think I'll just point out that you can press select to view the world map to get your bearings, and there's a sun keep you reach to the northeast of the map although you can't do anything there yet. The Tyrano Lair is the silver building in the middle of the continent.

The Tyrano Lair
I'd recommend equipping the rage band on Ayla, and the Silver Stud on Crono to make lightning attacks more affordable. Frog and Robo probably have some good multi-heal techs at this point, or you could rely on Marle. Anyway, clear out the first room of enemies and enter the right skull to go down some stairs. Fight some reptites in the next room, and you can open the jail cell or not, Kino will open it later anyway. Fight a couple more sets of reptites, and Ayla will bust Kino out, grab the Mid Ether in his cell then follow him to the entrance and he'll open up the left skull in the entrance hall so you can move on.

Step on the switches on either side to send the monsters tumbling to a lower level so you don't have to fight them. Head down the right path and through a door to find two eggs. The left one has a full tonic, and the right one will send you back inside the old jail cell where the monsters who you made fall down earlier will be waiting for you, and you'll have to climb back up. One word on fighting the monsters, shock the megasaurs, and attack the volcanoes to make them erupt damage on all the monsters on their own side.

Go down the left path and through a door to find a room full of teleports. Standing on some of the squares will get you into fights with monsters, and some will transport you around the room. The only two items worth having are the Ceratopper helmet and some Meso Mail, so once you have those you can move on. Just experiment and try stepping on each square if you're having problems finding them. Go through a room and past a sealed door, to find a room with two switches. The left one will send in some monsters to fight you, and the right one will open the skull so you can flip a switch to open the sealed door.

Save and heal once you've beaten him, and head up and through another area with a sealed door. Enter the right passage to find three switches. The center switch will make a save point appear, the right switch will make two terrasaurs appear, and the left switch will make a hole appear where the terrasaurs and the save point would appear. If you fall in either of the holes you'll end up in the previous room next to a sealed door, with possibly the terrasaurs for company. You can go straight through the skull, grab the Full Ether in the egg and flip the switch in the back to open the sealed door.

After you finish off the Black Tyrano, Lavos will crash to Earth and Ayla will name it "Big Fire". Azala will stay behind to be wiped out with the reptites, and Crono and company will explore the wreckage to find another time gate, guessing that the intense energy Lavos gives off distorts time and creates time gates. Your party will enter the gate to travel to 12,000 B.C., and wind up in the next chapter.

Challenging Lavos
If you go back and challenge Lavos at this point, you should get The Reptite Ending. You'll wake up at the start of the game where everyone is a reptite, including yourself. Presumably without your help Ayla wouldn't have been able to defeat the Black Tyrano on her own and Reptites would have ruled the past.