The score achievements can be done with any of the skulls, provided that your comfortable with their side effects. Now I'm aware that some of the par scores for Halo: Combat Evolved have been reduced so this guide should make things easier to decide which skulls/multiplier will work for you.
Now that the skulls are selected then comes the difficulty choice:
Heroic - 2x multiplier
Legendary - 4x multiplier.
For me I stick with Heroic and use the following skulls:
*In some cases I used the Recession skull just for the additional multiplier bonus.
Using the competitive score option gives you a general idea of how quick your going and how the points are being factored into your final score, but after a while your score will deteriorate when you start to pass the par time of the mission.
(One other thing to note that after 40 minutes of game time you will not earn any points for kills toward your score).
I would advise not trying to run through the levels and worry about the par time but instead make sure you have a comfortable cushion of points then after such time speedrun the rest of the missions so you can hold on to the minimum point values required to earn the achievement. Headshot/Multikill/Spree/Stick/Supercombine and EMP medals are great in boosting your point totals.
The only issue I noticed was getting through Two Betrayals/Keyes due to the fact the flood can overwhelm you if they are in great numbers and you don't have the right weapon to kill them.