Looking at the video, I think a Boom Boom or Rain of Fire Schneider would have been a better pick. More importantly, the player was using a Coolest that didn't really have any damage upgrades. It only had a 15% chance to critical, with no critical damage upgrades.
I've run through Upside Down on Insane a few times, and I'd say it takes me about 10-12 minutes with Lycus. I could probably do it a bit faster if I was sticking Aleph in things, but I'm usually just running around clearing the map.
In online play, Kuzmann's health is pretty high. It took us about 35 minutes to beat the map the first time at around 55% difficulty, though we were in a Squad, and probably didn't have the best team composition. Hopefully, the map goes a bit quicker now, but I imagine it will still take a while, and incentivizes people to pick the highest DPS characters that they can.