Now that I have an empty battle slot (Provided the fourth doesn't get abolished in the next week. XD...) I'll take you on. Note I'm just posting to reserve my place while I think up moves. So I'll edit this post in a second.
I'll send out my shiny male Skitty, Zelle, and my new Tropius, Saurio (Male).
========
All right, Zelle, lets start off with a nice Icy Wind to chill our opponents a bit. The wind might be able to hit both opponents, but if only one, aim at that Bagon. The cold will affect him more than the spider. Next lets help your partner out with Flash this should disorient the foes a bit. Finish up with an Ice Beam on the Bagon.
Saurio, take to the air so that it'll be a tad easier to dodge. Use Safeguard immediately to protect both you and Zelle from status elements. Next, use the Flash to your advantage, and while our opponents are blinded, rush in and use Toxic on that Bagon. As you swerve around, Aerial Ace the Spinarak.
Zelle (Skitty, Male): Icywind (If not both, Bagon) ~ Flash (Both) ~ Ice Beam (Bagon)
Saurio (Tropius, Male): Safeguard (He and Zelle) ~ Toxic (Bagon) ~ Aerial Ace (Spinarak)