Sniper rifles. She has a psi-shield thing that absorbs a lot of damage, but high-power weapons will knock it down with repeated hits. Use the biggest vehicle you have available for that mission, preferably a helicopter or better. Send at least 2 scout drones (or failing that, dogs) to act as spotters. Have them move into the jungle to spot enemies, and then have the snipers kill them with aimed shots in the dark.
When the area immediately around the LZ is clear, start setting the jungle on fire. Grenade launchers and incendiary grenades are preferable, but flare guns can work too if that's all you have. Target the big clumps of vegetation, but don't set any fires too close to the LZ that would make your guys visible. Keep going until your spotters eventually find the Avatar, and then have all the snipers focus fire on it. If you're using drones, be aware that if they get hit with her psi-laser thing it will vaporize them, which permanently kills them.