This requires entering the secret door at the end of the course. There is a timer above this door telling you how much longer you have to make it in. Its not too difficult as long as you are good with the route you take and use the fastest form of movement, which is: Roll->Jump->Slam. You will always have your roll button held down, and be jump-slamming as much as possible. Attack when necessary to take out enemies in your way, and remember that you can use this to extend your airtime, allowing you to time your jumps on the small platforms while still moving. You want to be moving in a straight line as much as possible. Here's my speedrun of the game to show what I'm talking about.
https://www.speedrun.com/Gizmo/run/z01ew69yAs for the room itself, there's some pretty tight platforming, but just take it slow and you'll be able to do it.