After the battle with Magus, you are pulled back into the past.
Chance for an Ending
Use the bucket (or telepod in New Game +) if you can beat Lavos now for ending "Dino Age"
Explore the Past
Now you can get new items at the trading hut.
The items for trade are as follows:
3 Petals, 3 Fangs = Dream Gun
3 Petals, 3 Horns = Dream Bow
3 Petals, 3 Feathers = Magma Hand
3 Fangs, 3 Horns = Aeon Blade
3 Fangs, 3 Feathers = Ruby Vest
3 Horns, 3 Feathers = Rock Helm
So, to get the new items (providing you already have three Ruby Vests and Rock Helms), you need 9 Petals, 6 Fangs, 6 Horns, and 3 Feathers.
Now go to the woods west of the Hunting Range where Laruba Village is. Go up until you see Ayla and the Elder. After that scene, leave.
Go to the Dactyl's Nest, northwest of the Hunting Range.
The path here is straightforward. First you encounter a Cave Ape and two Shists. If you attack the Cave Ape when the Shists are still there, the ape will throw a Shist at you. When you hit a Shist, it becomes a Pahoehoe.
Next you will encounter two Avian Rexes. Once you defeat them, climb the ladder to get a Mid-Ether. Then head downward. There is a chest below the Shists that contains a Mid-Tonic. You can avoid fighting the Shists by walking past them. Go up and climb the ladder, then exit right.
You'll encounter two Cave Apes and a Shist that blocks the ladder. You have no choice but to fight these enemies to continue, so get rid of them and climb that ladder. Climb a second ladder and head down. You can walk past the Shists to avoid fighting them. There is a Mezo Mail in a chest to their right.
Go up and climb a ladder. When you approach a second ladder, Avian Rexes will attack. After climbing the ladder you can get to the next area, where Ayla will summon the Dactyls. You can see an ominous red sparkle in the sky....
You will need to choose a third character to go with Crono and Ayla. I use Robo.