My strategy, which worked well and got me a score in the region of -01:57:00 (I can’t remember the precise time off the top of my head), was to play the 1st section as normal, try to maximise high score kills (executions, active headshots etc), use score cards, and grab as many normal weapons, grenades and ammo as possible. In the 2nd section, run through it and when you get to the helipad just fight from there. When you get to about half ammo (or whatever point you feel comfortable) pull the switch to close the door and continue fighting while the door closes. This allowed us to use the run method and maximise kills. The disadvantage is that you can’t really carry heavy weapons with you - it may be possible but will slow you down and be hard, and for characters with venom-based cards (Keegan mostly) won’t be able to use them as you’ll obviously be very far ahead of the venom - Keegan’s Ammo Resupply won’t replenish explosive ammo.
My friends and I favoured Fahz (who obviously used the Longshot and EMBAR); Clayton (who used the Torque coupled with Serrated Edge; and a Lancer); and Kait (who grabbed a Gnasher and depending on enemy spawns, can also get an Overkill as well). It’s also worth getting someone to carry an extra Longshot for Fahz too - the Lancer isn’t necessary for Clayton, but if you choose to run a different character then it might be a different story.
Also for the 2nd section, Fahz would lead the way - we found that there’s a small window for Fahz to slow down, stop and get some headshots on the Elite Drones along the way. During this time your team mates can run to both supply rooms and grab the COG tags and catch up. The timer on the enemy spawns means that you probably have around 10-15 seconds to do these little bits before the reinforcement spawns (DR1s, Scions, Poppers etc) start to catch up with you. You can further slow them by planting a grenade or two in the green stairway section inbetween the two fights.