Yes, because the Black Gummi horde has +3 Power defense. A Dispel medal is mandatory.
Based on your available medals, I would do this:
Piglet
Alice
J&S
Meowjesty
Flowbermeow (or a good ST Speed medal)
Note: If you get no Pester Jester spawns, then every fight you have has just one enemy. This makes the above setup so much more viable.
Alright then... now I just have to pray. I kept running through MoG 5 and every single time there were at LEAST 2 Pester Jesters. If that fourth one spawns with the fucking level 210 enemies then that makes the quest literally impossible. First one isn't actually TOO bad compared to the others... but if Paralysis strikes then yeah, that causes problems.
...This is super fucking tedious, jesus christ this quest is designed like shit.
Also, do Rare Enemy perks increase or decrease Pester Jester spawning? I was under the impression they decreased them, but... they've popped up a LOT.