Demonic Conflict is a Secret Mission located in Mission 5-Virility. The objective of this mission is to kill all five enemies within the one minute and twenty second time limit using only Demonic Weapons. Demonic weapons include the Arbiter and Eryx.
The best thing to do is use the Demon Evade ability to charge up Dante's power, then use the Arbiter to deal massive damage within a small area. The Eryx is not recommended, seeing as how it can only kill one demon at a time.