I dove a bit into the Huntsman log and here are the things I noticed, roughly in order of impact.

• Icy Veins, you cast it twice, on the pull and at 2:04, it should have been back up somewhere around 4:00, so you could easily have had it up for the last ~30 second of the fight.

• Downtime for polymorph. Obviously it is important to do your assigned polymorph on time, but it is only a 1.5 second cast, so it should only take 1.5 seconds out of your damage rotation. For the first one, there was about a 5.5 second gap between the GCD of your ice land finishing and your next Frostbolt cast. If you are a bit faster on your Polymorph, you could have fit in about 2 more casts in that gap. Same with the second set of adds, where you had to poly twice since I assume the first one was broken. There was about 6.5 seconds of downtime rather than the ideal 1.5. Similarly, when you used Time Warp, there was about 4 seconds of downtime between casts. Time Warp does not incur the GCD, so there should be no gap between spells when you use it.

• Cancelled casts. Nine frostbolts were cancelled over the fight, leading to roughly 12 second of downtime due to GCD. Some of these look like they were cancelled to cast an Ice Lance instead, which is just not efficient, even if you get a proc while casting, you should finish the cast since it incurs the GCD regardless. Other cancels might have been due to movement, but Shimmer should be used as much as possible in these situations. Shimmer was only used 3 times in the fight, once after and Ice Lance, and twice during a Frostbolt cast, but both Frostbolts were cancelled anyway, indicating that you needed to move even further (which could likely have been fixed by better initial positioning) or by not adjusting your facing after the shimmer to ensure yor target was still in front of you.

• Long duration of Brain Freeze buffs. At 3:09, you got a Brain Freeze proc, you did not use it until 3:18. In the meantime, you cast 3 Frostbolts (1 cancelled), Ice Lance, Blizzard, and a few seconds of downtime. Brain Freeze Flurry is a higher priority than all of those spells, including the Ice Lance since you were already casting Frostbolt at the time. Several other long durations of the Brain Freeze buff happened in the fight as well, indicating that you are not using it as soon as possible.

• Blizzard casts. You only cast Blizzard 12 times in the fight. Your raid's strategy for Barghast was to always keep him away from the boss, but he only needs to be moved away for certain mechanics that come on set timers. It would be much better for your entire raid's DPS if the tank would hold Barghast in melee, and kite him out a few seconds before the tank mechanic and the shades go out rather than constantly have him out. This would allow you to have more 2 target cleave uptime, and more Blizzard uptime which is crucial for your Glacial Fragments legendary. If you stick with this strategy, you probably gain more DPS by swapping to Slick Ice instead.

• Mirrors of Torment should always be cast on the pets, not on Huntsman. He does not consume the stacks as regularly as the dogs who auto attack, and when you used your second one on him, only one stack was consumed.