When you exit the ventilation shaft, you'll appear in a large planetarium-like room. Glide down to the platform with the tourbot pad, which will start a fight with a replica of Dr. Nefarious' biobliterator. All it will do is sit there and then look at you, firing a big laser. Simply Grav-Jump to another planet to avoid the laser, and keep firing at it until the thing is destroyed.
The destruction of the biobliterator will reveal a Grav Target, so connect it with the one on the other side of the room. Ride the beam that's produced into the next room, where you'll find the tourbot sitting there. Pass through the next room, waiting until the conversation with Talwyn is finished before the tourbot pad appears, then destroy the Bladeballs in the next room.
After clearing the Bladeballs, go to the next room, which is the Hall of Villainy, where you can read up on some of the villains in the series. In the next room is a button you can hit, which will turn on some music and make a series of platforms start to move. Use these to get to another tourbot pad, which will make the rest of the platforms in the room move.
Use the central moving platform to get across the move, jumping over the lasers, then use the circular ones (which flip on its side when they reach the top of the movement path) to reach the exit. From here, it's a straight shot to the room with the Dimensionator, where reaching it will start a cutscene.
