I brought in reinforcements with Zehir (44 units each) + 120 Thunderbirds. It didn't work the first time; I used the wrong magic.
But the second time, I did the following: I created a magic mirror and made the Biara unable to act. I cloned the Thunderbirds. They missed twice (I got lucky). I used Dominate on the cave lords (the summoned ones). And now there are none of them at all. I used Blind on the demoness. And by the end of the battle, I had 65 of my Thunderbirds and 104 summoned ones. The rest of my troops fell before the middle of the battle. The eagles were completely useless.
And in the end, 2 multi-shots.