If you burn the bridge while the big spider is on it, it takes some hefty damage. I also found out that you can engage the phase spiders without alerting the big one, so you can clear them out and be fully trained on the big one. As a note, my custom character was a fighter, and I and Lae'Zel both took battle master with the menacing attack ability. Turns out, spiders DO fear humans (and humanoids) after all, and if you get your whole squad to surround it when it is frightened, you'll get free attacks of opportunity from everyone.
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