After completing the previous Secret Mission and proceeding to the corridor encounter with Phantom in Mission 4, rather than going out into the courtyard with the lion statue, go right to the end of the corridor and enter the small room with the Divinity Statue.
This mission tasks Dante with killing 100 Phantom Babies for a Blue Orb Fragment again, but this time there is a shorter time limit and weapon use is not allowed. Beating this mission requires Dante to stomp on the Phantom Babies by walking over them: it is extremely easy if Dante has Devil Trigger, since Alastor's DT speeds up Dante's movement. If he does not, the Phantom Babies count as enemies, so the player can have Dante stand and taunt them to build up DT, then re-attempt the mission with a full gauge.