Surprised no one has made a thread yet with info on this stuff so I figured I'd start a thread so people can share what they've found so far and get some more obscure mechanics worked out. None of the dungeons are really that challenging but this ought to help ease first runs out somewhat.
Snowcloak
Spoiler: showFirst boss (Wandil) - Main gimmick of this fight is to deal with a stacking debuff that will freeze you if it gets to 4 stacks for 8 seconds. You'll take some ticking damage while frozen as well.
The main ways you get this debuff is from letting the bomb adds blow up (room wide explosion) and I believe from a move called Snowdrift. Snowdrift will cause a blizzard effect on your screen shortly after he uses it but I'm not entirely clear how you avoid it.
Wandil will also freeze the outer edge of the room he's in at around 30-35% and throw out aoes centered on random people.
Yeti - Lots of adds and tons of health. He'll use a room wide aoe that can only be stopped by hitting a snowball into him. Snowballs will also be the best way to damage him so the tank will need to try to get them hit by his large conal attack, Freezing Mist, so that the snowballs grow. Snowballs that have grown twice in size seemed to deal 10-15% of the Yeti's hp when they hit him.
Fenrir - Really straightforward fight. The biggest danger is Lunar Cry as it's not readily apparent that you need to hide behind an icicle to avoid it. Getting hit by Lunar Cry will freeze you for several seconds, inflict a decent amount of damage and a fairly potent DoT, and also make you a likely target for Eclipse Bite which he will always follow up with. Likely to kill a healer or lesser geared dps.
Qarn HM
Spoiler: showFirst Boss - Kinda like the Golem from the original dungeon in that there is the main 'body' that can't be hurt normally. The head, tail, and an arm can be hurt and broken to make the guy fall apart and this deals most of the damage to him until he reaches 5% and only the body remains. Adds will spawn each time he falls apart and he will reform after a set amount of time regardless if the adds are still alive.
Biggest threat on this guy is the quicksand which pulls you in and under while reducing your movement speed. He'll start off using just one pit but move up to 2 at once so make sure you don't get stuck trying to go the long way out of the pits. Moving away from their center won't move you up and you die instantly if you get submerged.
Second Boss - Cactaur(s). The main guy has a flower on his head and will use 100k needles at set %s (75%ish, ~55%, ~35%). 100k needles is stopped like Pom Holy and Pom Flare when he takes enough damage so this fight is a dps check.
The adds are pretty weak and easy to kill but two large versions of the adds will spawn in the fight. First large add will focus on someone (always seemed to be the healer) and will just chase them around doing fairly weak melee and 5k needles. The second large add will use Cover on the main Cactaur as he starts using 100k needles for the last time and this is where the main dps check is.
Final Boss - Summons 2 lines of mummies in random patterns that apply a stacking debuff that will not wear off until it reaches 4 stacks. The mummies have a larger hitbox than it would seem so give them plenty of room. Getting to 4 stacks will make you lose control of your character, force you into a coffin as you take ticking damage, and eventually turn you into a mummy that will also run across the room. You'll eventually regain control if you survive but it takes a good amount of time to wear off.
At low health (sub 40%) he'll start using a new skill that can also apply a stack of this debuff. His swords will glow purple and he'll turn and face a random party member while charging the attack but there will be no ground indicator. Just avoid staying infront of him while his swords are glowing. The final thing he does at this point is a skill that places a red marker above a random person's head. I didn't catch what this does exactly but it seems to apply stacks of the debuff as I went from 2 to 4 after the mark wore off on me.
Satasha HM
Spoiler: showFirst boss - Spits slime at two targets and will use Tail Screw on one of them. The slime slows and acts as a DoT while Tail Screw will always bring you to near death. Healer will need to dispel the slime so that the Tail Screw target won't die to the DoT.
He also marks the tank with Prey and will draw them in after 8-9 seconds. I wasn't able to work out of there was a way to prevent this but all he does after the draw in is stun you (and he might gain a damage and haste buff but I'm not sure on this).
Second boss - He'll charge at someone randomly and do a wide swing that knocks anyone it hits back. Afterwards he'll focus on someone and do a volley of shots. He'll summon adds throughout the fight that are pretty easy to deal with. The amount grows as his health drops and adds that grab onto you and bind you get mixed in. He'll run away at around 10% and summon a lot of adds that need to be cleared out to end the fight.
Kraken - I feel like there was something to this fight my group missed. It wasn't hard but he had a good amount of HP and the fight felt longer than it needed to be. His arms and tentacles are back from Hullbreaker and will keep coming back even if killed this time. They do exactly the same things they did before and go down fairly easily as well. He'll occasionally use Ink Blot, a large and short range cone, that blinds and deals 600ish damage to a tank.
Throughout the fight the Kraken also uses a move called Strange Tide. I'm not sure what this move does as I never took damage from it or saw any indication that there was something to dodge. His arms/tentacles will withdraw when he uses this and respawn a short time after.
If anyone has some clarifications on the new bosses or wants to share what they've learned about Shiva Ex and the Hildibrand fight feel free to do so. I put everything in spoilers since the post got kinda long as well.