While the map of Halatali appears to be one large area, it is actually divided by locked doors. Rather than open them, you use the Aetherial Flows which spawn after each boss to reach different sections of the dungeon.
In the second section, after you kill Firemane, you will encounter Chain Winchs hanging from the ceiling. Interacting with one will either spawn a coffer, a bomb which will cast self-destruct immediately, or a group of three lightning elementals. I recommend waitng until the monsters around the winch are dead before activating it, as the elementals can be painful.
Firemane himself doesn't do anything but spam Fire on the tank. Shortly after the pull, fire sparks called Damantus will start to stream in from two of the lanterns in the room. If they reach the center of the room, they will explode, dealing light damage to the entire group. While a few making it to the middle are no threat, you should try to prevent as many as you can to lighten the healing neccessary.
There is another type of add that will spawn in the same groups, called Noxius. These behave in the same way, except they deal much higher damage if they reach the center. Prioritize these to make sure that never happens.
I recommend having the tank stand in the path of one group of Damantus, while, if available, a ranged focuses on the other group.
Rather than engaging Guivre where it sits, pull it back onto the ramp. While in this phase, all you have to worry about is facing Guivre away from the group and moving out of Levinshower, a frontal cone effect.
After a short fight, Guivre will flee to the center of the room and go immune. It is important not to chase him, as the water will become electrified shortly. In addition to the electrified water, he will spawn three lightning sprites, which will likely go after the healer. Guivre will also gain the ability Electrify, which is a circle ground target ability on a random party member.
In this phase, you should stay on the ramp and focus on killing the elementals while dodging the Electrify attack. Once you have killed six elementals, Guivre will lose his immunity and switch back to the first phase. At this point, the fight will repeat itself until you have defeated Guivre.
Once you do, grab your chest and ride the Aetherial Flow to the final section of the dungeon.
This fight will already feel familiar, as Tangata merges the mechanics of the previous bosses. Shortly after the pull, he will cast Hot Horns, creating a ring of fire around himself and making himself immune to damage. Like Guivre before him, he will cast Firewater on a random player while in this phase.
But wait, there's more! While in this phase, the Damantus from the first boss will return, as well as a Fire Sprite for the tank to pick up. The DPS should focus on preventing them reaching the boss, as he is immune anyway.
This will repeat until roughly 50%. At this point, Tangata will cast Hot Hands, but without the flame circle or immunity. This will become a burn phase, where you will need to balance DPS between Tangata and the Damantus, while dodging Firewater.