Meta-game achievements are easy. Go on Normal and use the skulls Thunderstorm (all enemies are promoted one rank up--1.5x multiplier) and Fog (disables the motion tracker--1.5x), with maybe Tough Luck (enemies dive away more often from grenades, plasma pistol bolts, needles and vehicle splatters--1.5x) added in (you can also use the silver skull Cowbell to counter the Tough Luck skull a bit). If you're pretty good, you should be able to get at least a 2.0x time multiplier, which should make the whole thing easy.
Back on-topic:
There are two strategies that I found for beating the level "Cortana." One is to pick them off one by one until you can safely make it to the next area. The other is to find a route which offers enough protection that you can run through while shooting and chucking grenades to help keep them off your back. You may need to take a rest behind a rock to let your shield recharge before you continue. Also, always have with you a short-range weapon (Sword, Shotgun, or Hammer) and a longer-ranged weapon for the needle-throwing Flood (Battle Rifle or Carbine).
I think the Sword is preferable as a short-range weapon. If you can't find one or it doesn't have much energy, then a Shotgun. If you can't find a Shotgun or it doesn't have much ammo, use a Hammer.