Without using weapons or items, you have to step on 100 Phantom Babies in 30 seconds. Just keep running up and down the narrow space and you should win. It does take a little luck, though, as the Phantom Babies will wander around and spread out a bit. If you fail, keep trying. Eventually you'll get enough spider guts on your soles to win.
As a tip, if you're having trouble with this one, using Devil Trigger doesn't break the rules of the mission, so the faster run speed provided by Alastor's DT can make this mission much simpler.