I got some extra tips for a non-convetional strategy, in case you want to give Onslaught a shot again some time.
I did Onslaught with just one other person. Inconceivable, and we ran through the second chapter. Me (Architect) had two mid-level score boosts and my team mate (Blademaster) only had one. We made sure to hit only the second supply cache in chapter 2 for any tags, and we only got one there. We also made sure we both had Longshots for the active headshot bonuses, and we held our ground at the landing pad for a couple minutes. With this strategy we managed to get ourselves the highest reward with more than ten minutes ahead of the required time.
The reason I was playing Architect is because I find the ult to be super-handy on the Elite Drone hallway near the end, and said Elites are so distracted with the Hologram, we can headshot several of them with ease.
For Brawler, are you using Torch Tackle? This card will get you the most out of your tackle, but for the damage boost, the enemy must be set on fire first. This card does make it so the tackle sets enemies ablaze, so a second tackle on the same target is where the damage shines.