So this is the only Speed Run so far I've had trouble with. Watching speed runs online, it looks like everyone else had their gondala at the first platform before they got there while mine was stuck in the middle until after the hunter battle so I figured out a way to glitch that phantom into non-existence.
If you stay towards the opposite side of the platform (the entry side) and as the phantom starts circling overhead, run to the center pillar then to where the gondala lands, the phantom should despawn (since you hit a checkpoint with that movement). If you can't manage to get this to work, you can easily kill the hunters by meleeing them in the face and when they glitch around quickly no scoping them with a beam rifle. Gernade jump accross the gap to shave off about 5 seconds. (If you don't think you can make it, don't try, I had a 43 second margin on my run.)
I used a beam rifle to snipe the elites on the gondala ride, but if you are better with gernades or whatever, do your thing.
In the room before the first elevator make sure you run up the ramp before killing the majority of the jackals. If you don't a tone of drones spawn and those are always a pain for me to kill quickly. If you head to the top of the ramp and take out the grunt, the drones won't spawn when you finish off the jackals.
From here its sprint sprint sprint. Stop for nothing, kill nothing. Get to the next elevator ASAP. From there get to the gondala ASAP. Start it moving before killing stuff off. Pick off the hoverpack elites however you see fit (i opted for sniper again) then gernade jump off of the gondala onto the platform, skip the cutscene, run into the bastards room, mount that guy and go to town. Again, killing nothing on the way in. After you punch him out, be careful as the sword elites will still chase you around for ~15-20 seconds.