One could always play a game of pass the baton. Basically:
Alice barked an order at her houndoom, barely getting out of the way as Bob's meowth attacked Chris' golduck. Chris cursed and yelled at Dan, and Dan straightened his back, his tauros attacking Bob's meowth with renewed vigor. Chris then turned back to Eric, who was helping Felicia against Gerald and Hugh, their water pokémon soaking the brothers' fire pokémon.
Just as Chris is about to order his golduck to attack Eric's blastoise, vines wrapped around the blue bird and a voice rung behind Chris.
"You're mine." Ivy motioned to her venusaur and Chris' golduck gargled as the giant plant-reptile started to squeeze the air out of it.
End random five-minute example.
As you can see, the scene shifts kind of like a running take on a film set (watch the absolute last scene of the British cop series The Bill, and you see what I mean), which can add to the chaos and disorientation that a large battle would bring.
Then the chaos takes a breather as one focus on the main battle (Chris and Ivy) for a while, and then Ivy is nearly knocked out by Jake's gligar and the baton is passed around again, until it gets back to the main battle. And then Chris ends up between Karl and Laura's pokémon and has to dodge, and the baton makes another round before coming back. Rinse. Repeat.
However, you might want to keep the high-lighted characters under a certain number, and not go all the way to Xander, Ylva and Zane. Just mentioning some background noise and dodging stray attacks (or avoiding other combatants) during the main battle should suffice.
One can also combine the above technique with others, such as switching POVs when one switches scenes, showing the battle from another angle.