Geez is Shuckle ridiculous. I have a team consisting of Mega Slowbro, Swellow and Swablu and I could not catch him (frankly the bonus for spare moves isn't that much of a help)
I'm going to guess based on your team that you're not far into the game and are just using whatever you have on hand, right? I'd suggest going full-Pyre team: Combusken, Charmeleon, Torchic. Conversely, I'd ignore Shuckle for now and just spend the rest of the week unlocking normal stages; the daily Pokemon always appear for at least two weeks in a row, so Shuckle will return next Wednesday. Save your coins and jewels, as you've got some tough stages ahead (M-Mawile, M-Glalie and M-Gengar will test your sanity). If you can make it to M-Gengar before the end of next Wednesday (since I'm basing your progress on Swellow's stage, that's about 62 stages beyond him) and win, M-Gengar's effect (it Mega evolves in 3 or 4 matches, the fastest mega evolver in the game with one of the most powerful effects) and two super-effective Pokemon would trivialize the stage.
Edit: As for Regirock, for those still struggling, his stage
has been made easier as of the new daily Pokemon update. Prior to it, the disruptions that fell were a mix of rocks, steel blocks and Regirocks. After the update, you do not see steel blocks outside of the very start of the stage and his final disruptions. As someone on gamefaqs posted, it is possible to S-rank Regirock itemless now by taking M-Mawile and two of your strongest mons (Block Bash ability not even necessary) while leaving the fourth slot blank (Regirock will be considered your fourth Poke in this case).
For those curious, here's a video link to the strategy: