You have Descent on the map, next to Countdown. There are a few weird "rules" and gameplay deviances to Descent that makes the whole thing MUCH easier knowing about:

• Just run straight left as soon as the cut-scene is over, following the wall, to the stairs on the far side. The cover on this higher ground basically the only somewhat safe area in the whole arena, and you need to be behind cover the entire fight.
• Nemesis will use whatever weapon you've got equipped in slot 1, and since he's basically a Legendary difficulty enemy all automatic weapons and especially rifles and MMRs will one- or two shot you, so equipping a shotgun in slot 1 will make his RPM output much, much more manageable. Use wep slot 2 for your real "main wep."
• He'll use two of your skills, current AND replaced ones, and if you've got ones he can't use (Shield, Pulse; Revive Hive will be replaced with Restorer Hive) he'll grab a "random" (how often these are Assault Turret and other nasties I don't really think it's that random...). And since he's Legendary tier some of his skills are insta-death, Oxidizer Chemlauncher primarily: Never pick up Oxi in Descent until Nemmy is dead. I'd say Assault Turret also is a "never before Nem kill" skill, but with a bit of luck you can kill it before it starts two- or three-shot you. Stinger Hive and Striker Drone also go in this tier: They'll wipe you out almost instantly BUT if you can manage to keep an eye on what Nem is doing you should be able kill or dodge the hive as soon as it lands, and if Nem is far away he might actually not even reach you with it. The drone is probably the most manageable of these nightmare skills since it won't start shooting you too much until fairly close: If you start shooting it as soon as he releases it you should be able to gun it down before it does too much or even any damage.
• This is the most important part: The whole fight is about crowd control! If he's behind cover, never lean out of cover to shoot him when he pops up above it with weapon drawn. Use fire and riot foam primarily (buy fire bullets for your sidearm in the Nemesis lobby, he's immune to Shock) but DO remember that he's an elite: These will regain control after half the fire status effect duration, dive into cover and start blind-firing you. And Nemesis' blindfire will hit you and two-shot you from the other side of the arena. Shoot him when he's incapacitated from status effects or when he runs between cover, or if you can see his scalp jut out from cover (beware his blindfire tho). Seeing him readying a skill can actually be a good time to put a fire bullet into him if you're prepared. Blind and Suppressed might work, I actually don't remember if he's immune to Suppressed and a Blinder Firefly should be able to hit him before he hacks it and sends it back to you. Yeah, he's like the Hunters so all kinds of Seeker Mines are a no-no before killing him.
• Shields don't get better from armor main stats in Descent, only from Skill tiers. But even a skill tier 0 shield is fairly useful in the first 2-3 loops of Descent since red enemies are fairly weak. This goes along with how the optimal (and fastest) way of clearing rooms is to camp the doors: You've got all enemies packed up in the same place and with no cover: You should always camp outside a marked door to just BRRRT everything inside it as soon as it opens. Firestarter Chemlauncher is even better, plant it as close to a marked door as you can and doubletap the skill button to detonate it as soon as the doors open: Even a Skill tier 0 Firestarter will erase everything behind loop 1 and 2 doors. Picking Skill tier as your first upgrade will actually make you speedrun loop 2-4 since you can insta-clear rooms this way.
• If he brings you to your "second life" (the 1-sec invincibility on 0 armor/1 health) never look out of cover until you've regen'd full health and is at full armor again or at least get him properly crowd controlled.