If you joined Magma Gang, you'll get a Buizel during an event. Buizel has aqua jet, a priority move which can OS anorith.
But reading your team comp, I think you choose the Aqua Gang because you have Ponyta (maybe there's another way to get one at this time of the game than joining Aqua Gang, that's why I talked about this strat).
Why not use this strat differently, with a pokemon with good speed and a Water attack (I don't think water type is needed, because Rain + Anorith low defenses should be enough to OS it) and the focus sash to avoid dying on the turn he attacks you. You'll need good speed to be sure to attack before Shelly's second pokemon. Keep in mind that the telluric seed gave Anorith one turn of Spiky Shield.
This strat should also works with a Steel or Ice attack.
Another strat that worked for me is Swalot. Stockpile, Toxic, Take Down and Sludge. Shelly's Pokemon don't have an attack super effective on poison type. If you're able to set up Swalot on the first two pokemon and have some potions, you can tank all her team easily with Swalot. I generally combine both strats (Swalot + a Water attack on Anorith) and Shelly is no big deal with this (but she gave me a lot of trouble in my first run too, you're not alone pal).
