Toon Decks absolutely crush the Gemini deck. Just don't attack monsters. If you can get a 6 star or above Toon on the field, you win. Do all toon monsters and a few protection spells/traps like Econ, Windstorm, Half shut, etc.
Currently 17-2 with this deck. Can be adjusted minorly to help with fairy and warrior stage missions. Can also be boosted stronger if you replace some of my Warrior and fairy monsters already in the deck with stronger attack as effect monsters.