This challenge quest is all about the enemy's status effects. There are only 3 different enemy types and all of them have area attacks that can inflict either paralyze or confusion.
Carbuncle won't be using magic reflect ability in this quest, but it has confusion up passive and will be using it a lot.
Arcana Serpent can inflict paralyze from one of its ability and also has a decent ranged counter ability that can inflict paralyze. The snakes has paralyze up as well.
Mindflayer has the widest area attack that can inflict paralyze, and possibly the one with the highest chance. Also has a single target poison inflicting spell.
This quest is much more doable if you have a tank to avoid getting your entire team from paralyzed/confused. Make the tank go to the edge of one side, away from the rest of your team, and tank all the status effects.
White Marshmallow Miniature can help get some resistances, but it might not help that much due to their high chance and multiple attacks. It's obtainable from the previous Carbuncle raid.