Nice content PiergeironPaladin229!
I’ve outlined the exact ordering of Argathakul’s attacks in this guide here: A Dance with Dragons: retsamerol's step-by-step guide to dancing with Argathakul
So, in my opinion, it isn’t a formation so much moving your characters to a space they won’t be attacked for 2 turns (so that they can attack one turn, and then move the turn after).
Another thing I’ve noticed: The boss behaviour is predictable immediately after you have brought the boss to their “bloodied” status, i.e. reach less than 50% health.
That means that rounds when you take the bosses to less than half their hitpoints deserve special consideration.
I haven’t noticed anything special for Harkald Firesworn. So long as you have a melee character in the first row, he always engages in push attack. I would say a single melee character with a character behind bracing, is sufficient; you don’t need 2 melee characters in the front row.
Your post deserves a thread of its own