As far as I remember, the annoying pokes I had to deal with Shelly were her Yanmega and Volbeat.
Anyways, level up some of your mons to the 30s, maybe try to catch a Geodude/Graveler or maybe grab Emolga/Litleo for this badge. Be wary of the Anorith spamming Rock Slide, Heather the Yanmega, and Bugsy the Volbeat.
EDIT: Forgot to say Hariyama, Meowstic, and Noibat won't be doing that much this battle probably.