Your fighting on a circular platform, so it's very easy to get flanked. To help your cause (unless if your going for a leaderboard score) give Jack the GAC armor, and make Shadow invisible.
When the levels begin, fight in a place that's somewhat defendable, so at least your not completely surrounded. Guns always seemed to make it worse for me, so I just basically fought my way through with the occasional headshot/"massacre" shot to add to my score. Just keep slugging/shooting your way through, performing as many "stylish" kills as you can (headshots/takedowns) and by round 6 you should have it.
You still get it even if you die, so unfortunately, I can't help you with the GAC Tank issue that appears in Round 6…