Just to clear this up.

The problem you are most likely having with the Sch level 60 quest is not related to your gear but is likely related to the mechanics of the quest.
In the instance there are several NPC's. These NPC's get debuffs which if not removed will cause you to fail for what may seem like no reason. It does happen and if you dont see the debuffs then you will be left wondering why you failed the quest. There are quite a few NPC's and more join you as the quest continues.

The best course of action to complete this quest without too much of a hassle is to keep checking all the NPC's throughout the fight and use Esuna to remove any debuffs they get. Adds will spawn and you should kill them as fast as you can, however mind the NPC's debuffs while doing so.

Keep these things in mind and you will be able to complete the quest without too many issues.