First of all you don’t attack an ancient site if you are not prepared with a good squad, 10-12 Hopelites and 1 Cyclops is not easy.
You have to try to activate one or two Hopelites each time, and of course Cyclops at the end of the mission.
If you want to fight using long range, you need snipers with high accuracy and Pythagoras SR, the shields are not covering all their bodies, a small portion is over the shield, there is where you aim
But Stealth is the safer aprroach, you include infiltrators and they could finish many hopelites before activation, or using vanish:
Decoy is also interesting, those beams are dangerous:
More tactics include hide and hit:
And of course lot of Overwatch, because they move towards you:
And dashing and SG (Harrower even better) is a great resource:
Also Heavy using mounted weapons, Destiny III is high precision
And for Cyclops, Rage Burst with Hel II Cannon, or using Acid Cannon, one turn and done, if not snipers, and hit the head to avoid the beam