For the double battle with the two unknown, I suggest you use Volcarona, hence there two starting pokemon would have problem defeating it. Next, I'd suggest you'd try to use quiver dance for Volcarona, maybe three or four times (I believe that is more than enough), and I promise you, it would feel like taking candy to a baby.
For Cain and Shelly, I focus all my effort to Shelly first hence bug types are easier to kill and more annoying if it prolongs. Shelly's Ribombee will first try to use sticky web, which you wouldn't want to happen, so I suggest to kill ribombee first using your first two pokemon who has priority move, hence ribombee has very high speed. Metagross with bullet punch and Mamoswine with Ice Shard.
The first unknown challenge you'll also face would be using dark type, so bringing bug and fighting type would really be useful.
I hope this helps.