So, I just spent a good chunk of my day on Jawks of Hakkon (PS4) and could not get past Hakkon even on casual. The team all had good armor with cold resistance; Varric, Dorian, Cassandra, Male Dalish 2H Warrior Inquisitor. I'm fine until I take out the four mages and disrupt the ritual. I'll get Hakkon down to about 40% health then he manages to take everyone out one by one.
I'm also at a point where I can't go back anywhere and I'd have to restart most of the campaign to swap out team members. Of the remaining folks I can bring, there's Vivienne, Blackwall, Cole, and Bull, It's a post game save so Solas is gone and I kicked Sera from the party.
So tips on taking out Hakkon? I haven't even gotten to the dragon yet :/
Hakkon is the dragon. But the fight you're talking about is significanty harder than Hakkon.
Anyway, this guy has tons of health. You need to do a ton of damage to him, and ideally quickly. So you'll need multipliers.
I did it (on Hard) mostly just with Static Cage combined with Flask of Lightning and some auto-attacks from Sera. If I'd had Cole there, Mark of Death would have made it fairly simple.
The reason the fight gets progressively harder is because the fires start going out, so there are fewer and fewer places for you to be in the battlefield where you won't start taking cold damage just from standing there.
Don't forget those super cold resistance tonics you get in JoH. Those are useful.
I don't have any specific advice for this fight with a 2 warrior party. Does Varric have Throw Everything? That might come in handy (though again, that's best when combined with damage multiplying abilities like Static Cage or Mark of Death.
This fight you're having trouble with is the only fight in all of DAI (so far) that rivals the difficulty of the more challenging fights from DAO (like Jarvia or Caridin). I think the reason people are having so much trouble with it is that nothing else in DAI required you to use your characters together efficiently.
The first time I tried this battle, I had with me Solas and Cole, both of whom were spec'd for cold damage, so they were basically worthless. But I didn't have any trouble getting there with that party, suggesting that there wasn't anything like a steady difficulty curve - just that one fight at the end that was way harder than anything that came before it.