The score achievements can be done with any of the skulls, provided that your comfortable with their side effects. Now I'm aware that the par scores for Halo 4 have been reduced so this guide should make things easier for the decide which will work for you.
*(I haven't tried any of them on normal yet so let me know if they work)
To obtain each of the par scores achievements in Halo 4 I recommend Heroic (2x Multiplier) along with the following skulls:
*If I'm feeling lucky I might throw in Iron but only on special cases.
As long as you have a precision weapon in hand you should be fine, but never pass up on the power weapons if available.
(One other thing to note that after 40 minutes of game time you will not earn any points for kills toward your score).
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.
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. Blowing up all vehicles will also give you more points, but only do so if time permits.