To actually access the mission, Dante has one chance to cross the broken section of the bridge without falling down: falling prevents the mission from activating. Luckily, this secret mission is right at the start of the mission it is in, so restarting does not lose a lot of progress. The easiest way to get across is through the use of Air Raid or Vortex.
This mission is another with a Blue Orb Fragment located high in the air. This time, it is precariously placed over the broken part of the bridge. The intended method of getting it is to use the pillars created by the Death Scythe in this area to get Dante high enough to Air Hike up to the Fragment or Enemy Step off the Death Scythe, though this is far easier said than done and missing the Orb is likely to drop Dante into the water. Doing this fails the secret mission, and it cannot be re-attempted without reloading the save file.
A much easier way to accomplish this mission is to kill the Death Scythe to restore Dante's DT Gauge, then jump up onto the porch structure over the door to the cathedral. From here, use Air Hike or a wall-jump to get some height, then trigger Air Raid. Dante should be at the ideal height to fly back and grab the Fragment. Alternatively, Dante can taunt the Death Scythe for DT, grab the Fragment, and then defeat it for a DT gauge refill in order to fly back across the broken bridge.