The secret area that holds the Blue Orb Fragment is across from the tunnel entrance that is reached by using the first batch of Grim Grips in this room. To get to this area you'll need to use mid-air attacks to cross the gap. First, stand on the wooden platform and face south. Next, use Streak 2 to propel Nero forward, then use Roulette Spin and immediately after that, use Air Hike. Hopefully you are above the platform, or at least close to it; use Roulette Spin again if necessary. This is a tough one to get and might require a few tries, but if you're using the right skills, you'll get it eventually.
When you're ready to proceed, go through the tunnel entrance and clear out the Scarecrows that spawn. Afterwards, hop up the ledges at the northern end of the room. Turn left into the dead end and grab the Vital Star S there, then smash the board up ahead and follow the tunnel to its end. This video is from our unofficial game guide. You can view the full guide here