The eighth mission is "Cortana". The easiest way to get this achievement is to play on Normal with a few skulls turned on.
First of all turn on the "Catch" skull. This level only has flood enemies on it, and the flood don't throw grenades. Turning on this skull won't make the level any harder.
Also, turning on "Tough Luck", "Fog", and "Famine" will increase your score but won't make the level much harder. Famine especially shouldn't make the level any harder because there are weapons with full ammo lying on the ground all over the level. In the room where the "Tilt" skull is located, there is a Gravity Hammer with full ammo in a lower room located almost directly under the skull. It works very well against the flood and will last you for a good portion of the level before running out of ammo.
With those skulls turned on while playing on Normal, you should easily be able to score over 15,000. Don't worry about the time bonuses. Take your time and hang back, trying to stay alive, and killing everything before moving on. If you take it slow and ensure you don't die too many times, you will get the necessary score, even with only a 1X time multiplier.
If you're still having trouble getting enough points, consider either turning on "Mythic" and/or "Tilt", or trying to finish the level with a higher time multiplier.
NOTE: This achievement can also be unlocked in coop, but you still must score over 15,000 individually. Turn on Free For All scoring instead of Team scoring to be able to see how many points you yourself have while playing the level.