The Tyrano Lair is the last dungeon in Prehistoric times. The opening hall has two passages. The one on the left, leading up, is initially closed. Instead head down, freeing the prisoners below. Once Kino is freed, head back up and he will unlock the stairs leading up.
The switches on the second floor landing will drop the enemies into pits below. The right path leads to Treasure, while the left leads to the next floor. Be careful when collecting the Treasure—touching the right chest will drop you into a room containing any Monsters you dropped previously.
You'll run into an amusing enemy starting in this section, the Volcano. Reptites will sometimes kick them, making them erupt on the party. You can turn the tables on them by hitting them yourself, causing them to erupt on their own allies.
The western part of the second floor includes a large room with some strange properties. Encounters will pop up without warning, and you will be teleported around as well. Trial and error will get you most of the Treasure, but the Meso Mail can be tricky. From the entrance, head north until you hit a pit, then directly east to end up in the southwest corner. From there, move east again to appear in the northeast near the chest.
On the third floor, head past the gate into the eastern room. There are two switches in here. Either one will open the skull, but the one on the left will also cause enemies to appear. Hit the switch inside to open the gate outside, which leads to Nizbel II.
Nizbel II initially ignores you, but will attack when you try to move on. Unlike the original Nizbel, you can deal reasonable damage to start with. However, his defense increases when he is attacked. Have Crono counter this by repeatedly electrifying him. Don't forget to save after you win—you're not done yet!
The fourth floor is similar to the third, with a locked gate in the center and a room to unlock it on the right. This room has three switches, though. The center switch creates a save point on the left side. The left switch removes the side floors, while the right switch drops two Terrasaurs into the room (which will fall through if you've removed the floors). To open the skull, just go up to it and use it. The switch will again open the gate.
The BlackTyrano fight is more of an event than a typical Boss fight. Equip any Ruby Vests you have before the fight, to help against Fire Breath. At first, the BlackTyrano's defenses are basically impenetrable—you need to defeat Azala first. She has high Physical defense, but is vulnerable to magic. Ayla can be more effective using Dual Techs, depending on who's in the party.
Once Azala is gone, the BlackTyrano will lower its defenses and start counting down to Fire Breath. This is a nasty attack, so heal up before it goes off. The Rage Band is especially nice in this fight because every time the BlackTyrano counts, it is considered an attack (and can be countered).
After the fight, there is a fairly lengthy cutscene. In the end, you'll find a new Gate leading to the final Era of the game—the Dark Ages.