After you find a way to fly around the prehistoric world, you should look for a way to return to your own time.
Go to Tyranno Lair
Fly over to the Tyranno Lair, in the middle of the lava field to the east.
Enter Tyranno Lair
Inside, go up (avoiding the Cave Apes by staying centered between them and not staying in the line they walk for long), into the open skull, and down the stairs. Fight the Reptites, then open the cell. Then continue right and fight the Reptites. Go down.
Fight the Reptites by the cell, then check on Kino. Before following him, go into his old cell and open the chest (Mid Ether). Then go up the stairs, and back to the room with those skulls. Go through the one that Kino opens.
Go right, step on the switch on the floor to get rid of the bad guys. Then go down through the door. From where you enter this screen, go straight right to avoid a fight. DON'T open the chest on the right, it's a trap. Get the left one (Full Tonic) and exit, back into the room where you stepped on the switch.
Now go left, step on the switch to get rid of these guys, and go out. The Reptites here are avoidable.
Now in this big room, certain tiles will warp you around when you step on them, so there's a specific route to get all the treasure and then get out. Here's what to do:
First, walk right until you're against the far wall. Go up past the first gap in tiles, then AS SOON AS you get past the second gap in tiles, walk left to be transported. Go up and open the chest (Revive).
From there, walk down about five tiles, then right. You're aiming for the tile that sticks out at the corner part of a gap. You'll be transported. Go up and open the chest (Meso Mail).
From there, walk left across the little bridge until you're transported again. Go up and open the chest (Tonic).
Now, walk down, and when you hit a gap in tiles, go left, and when you can, down the little bridge, to reach another chest (CeraTopper).
From here, go straight up, then as soon as you can, left, and you'll be transported to the stairs out of here.
Be sure to equip the stuff you got in this room.
Keep going and you'll be outside. It's possible to avoid all enemy encounters out here, but it's tricky. First thing, you'll want to hug the wall above you when you walk right. As soon as you near the locked door, go straight down into the little piece of ledge, and hug the bottom as you walk right, until you're about halfway along the longer bottom piece. Finally, go up a little and then right. You should have a clear shot to the door above.
In here, step on the switch on the right to open the skull. Go through and hit the switch on the wall. Now go back outside.
To avoid a fight, walk down a ways, then left. No matter what you do, when you approach the now-unlocked door, you'll have to fight. When that's done, go through.
Walk around Nizbel and use the save point and a Shelter. When you try to exit north, he fights you.
Volt Bite (a.k.a. Thunder Chomp) will lower Nizbel's defense, so use that continually. Leave Robo to heal once Nizbel releases the electric energy, then repeat. Keep HP above 200.
Use that save point and a Shelter again, then go up those stairs and outside.
Once again, it's possible to avoid all enemy encounters out here. First, walk down so that when you walk right, you'll hug the bottom of the bridge. Go about halfway across the bridge, then go up and hug the top. Go right until you're *almost* at the end of the SECOND bridge. From there go down and hug the bottom, then right, and then straight up through the door.
In this room only hit the upper switch, to make the save point appear. To open the skull, all you have to do is check on it. Go through, get the chest (Full Ether) and hit the switch. Then go back out and use the save point (and a Shelter if you need to). Now exit.
To avoid an enemy, walk down so that when you walk left, you'll hug the bottom of the bridge. As soon as you're a little ways on the bridge, walk up and hug the top. Then walk left, and when you can, up for an unavoidable couple of fights.
When that's over, walk up through the door. Go up and there's Azala. When he's done, go up and get the two chests (left: CeraTopper; right: Mid Ether). Finally go up through that door.
Azala and BlackTyrano
First you want to get rid of Azala, and to do that, just keep hitting him with Lightning (not Lightning2). Don't have Ayla do anything while Azala's still there. Keep HP above 250. If BlackTyrano eats one of your party members, have Robo heal him/her right away.
When Azala's gone, wait for BlackTyrano to "remove def" and "store pwr" (which he may do before Azala kicks the bucket). When he does this, a countdown will start. Attack as many times as you can with Volt Bite, and leave Robo to make sure everyone's HP is above 350. When BlackTyrano does his major fire attack, have Robo heal everyone up, then wait for BlackTyrano to remove def again to start hitting again with Volt Bite.
Go into the Lair Ruins and check the gate to go through.