You will be able to tackle this Challenge Quest after gaining permission to venture below the Naraku's 3rd Stratum, though it can prove quite challenging without preparation!
It may be a good idea to wait until you defeat the Minotaur boss and gain access to gun equipment for the main character. Meanwhile ensure that at least one demon in your party has a Gun attack skill of their own, as the Calamity Hordes you need to defeat for the duration of this quest are weak to Gun attacks.
Once you accept the quest, heard for Naraku's 3rd Stratum and wait for the Calamity Hordes to spawn at the following locations. Note that it is highly recommended that you save before each of the five battles, as there is always a chance that the Calamity Hordes will act first with powerful skills like Blight; things can go bad fast!
- Near the sign you encounter from the stairway leading to Naraku's 2nd Stratum
- Go past the doorway next to the sign and in the next room, crawl through the southern hole leading to a dead end with a treasure chest
- Return to the previous room, crawl through the eastern hole, then crawl through another hole leading east (i.e. the path you normally use to bypass the poison once you open the path) to arrive in the long hallway with a set of doors up north; head south instead and climb the ledge to where you can randomly find a relic
- Drop back down, then head north past the next set of doors and wait in the area you first emerge in
- Continue north and climb another ledge leading to a treasure chest
Note that you can defeat the Calamity Hordes in any order, but you must defeat all of them; upon beating the last horde, you'll immediately need to fight the Fiend Demon David (hope you saved like I told you earlier)! David uses dark and status skills like Mamudo and Pulinpa to make a real mess of your party, but fortunately he is weak to Zio skills. Defeating him finally completes the Challenge Quest.
Note that while this is a real nailbiter of a quest at times, it's well worth completing it as it also unlocks David as a Special Fusion (Lvl 22 required)!