Archons are not really difficult to fight, it is just that, you can barely hit them once you meet them initially. They are as slimy as a Viper, as they can either dodge your shots or just graze around it. Thus reducing your chances in bringing them down.
They have two skills, Battle Frenzy and Blazing Pinions. Only the former skill pose real threat,
Battle Frenzy allows the Archon to have a free Movement if they are attacked. This could be a good thing if your soldiers are scattered all over the place, in good positions, under Overwatch. Otherwise, your soldiers are going to get murdered when you start hitting Archons and they be surviving!
Blazing Pinions is an attack that has two phases. The Archon will rise into the skies and fire missiles from its back and those missiles will arrive a full turn later. The location where the missiles will crash will be indicated, and then, you have time to scram, run away, hit the Archon (which is difficult because the Archon gains massive amount of "dodgery".) The missiles are similar to grenades with its blast radius and damage. Blazing Pinions are not interrupted by merely hitting (by hit or by graze) the Archon, unlike the Vipers' Bound. You do have to kill these Archons to stop the Blazing Pinions from connecting.
Archons are only dangerous when your positioning is out of whack. Archon's melee attack are very dangerous because of their mobility, as they can reach any of your soldiers with ease. Without a properly overwatched soldier nearby, these flying Ancient Egyptianesque units will just eliminate your squad uncontested.