Use the Time Traveler's pass-through ability to move throw the rock formation and keep heading to right to find an unpowered time machine.
Climb the ladder to the right of the time machine to find a Cave Painting.
Head left to find a rock you can push. Move it so that you can reach the fuse box above, and take the power cell.
Head back down the ladder and head right to find another. Descend it and head left to find an empty fuse box. Place your cell in it to reactivate the time machine.
This time machine can be used by any party member, and any object within the blue light will also travel. Nifty, eh? First, travel to the past.
Climb the ladder up again and head to the movable rock. This time, slide it under the drip you pass on the way to it. This prevents the rocks from forming in present day. Switch to your teammates (who are in present day) and move past where the rock would be to enter the main area of the level.
Use the Time Traveler and head to the future. Pass through the security door to encounter your rival. Be sure to hit the green button to open the door for your teammates.
From your rival, head right. When you reach a ladder, descend. Go down through all the levels until you reach the lowest. Head right to find a dinosaur exhibit. Hit the button to "smell like a dinosaur."
With the dinosaur scent on you, head to the past. Go the same spot as the future exhibit to find a living dinosaur. On your way there, hang right after the first ladder to find a Cave Painting. When you reach the dinosaur, he chases you due to your current smell. Lead him to the left until he can't go further.
Bring another teammate into the past. Come to the same area, but stop at the ledge above the dinosaur. Go left to find Thog, who builds wheels. Push his current model to the right until it lands on the dinosaur, killing it.
While still in the past, head back up the ground level. Move right to find a rolling rock blocking a drip. Pull it away from the drip and hold it there.
With a second character, head to the present. Go to the spot where the rolling rock would be to find a well. Use the crank and hold the bucket out of the water.
With your third teammate, head into the future. Go to where the rolling rock or well would be to find a bucket on display. Pick it up.
With bucket in hand, head down to where the dinosaur would be. Ignore the key on the way down; it's guarded by a laser. Also, if you go to where Thog would be, you'll find a Cave Painting. Where the dinosaur died, there is now oil. Scoop it into the bucket.
You've probably noticed that funny-looking machine near the Time Traveler's rival you've past a few times now. Pour oil into it to activate the nearby elevator.
Hit the call button and ride the elevator up to find a tire. Ride back down and take the tire to the time machine. Travel with it to the past.
Push the wheel until it falls off an edge and rolls down to the dead dinosaur. Thog will see it and run up to it. Roll another rock wheel onto him as you did the dinosaur, and it'll crush him. This erases the Time Traveler's rival from the future.
Head back to the future and move to the laser-guarded key we told you to ignore. With the rival gone, no one can activate the lasers. Grab the key and return to modern day.
Move left and open the series of doors to exit the level.