Yeah, but it doesn't last that long against it. Especially when you use it twice on him. First time you use it, it'll last about 3 seconds, and it decreases rapidly from there. The bigger/stronger something is, the less time Stasis will hold it.
He was using the Eviscerator, the Phalanx Heavy Pistol, and the Locust SMG.
Honestly, it may sound odd, but the hardest class to do this on Insanity with is the Soldier. Every other class has either some way to protect themselves, distract the enemy, or get out of a tight spot, EXCEPT the Soldier. Adrenaline Rush doesn't give any health regeneration, nor does it distract the enemy, and it doesn't make you zip from Pt. A to Pt. B like the Vanguard does.
Engineer has distractions. Adepts have Singularity (which can destabilize an enemy at the very least). Sentinels have Tech Armor, which is broken for Insanity. Vanguards have charge, which will not only give them a huge shield boost, but it will also move them to a different location if they have too many people around them. And Infiltrators can turn invisible, making every single enemy stop shooting and stand still.
Infiltrator and Engineer are by far the easiest classes to do that part on, no matter the difficulty. Sentinels are just too easy for Insanity anyways, I'm ignoring them for this lol.