If you play on the "Recruit" difficulty, which is the easiest one in the game, then this achievement will probably be difficult to reach. Whereas this difficulty you have to worry about the amount of kills, head shots and such you obtain during the length of a mission, even on the default difficulty, you will obtain 10,000 points upon completion. It should be a breeze.
If you MUST play on the easiest difficulty, or just want to solidify your 10k, then attempt to finish a majority of the challenges on a given level. Each challenge, regardless of difficulty, is worth 2,000 points. Every mission (not sure about Strike Force) has a challenge to not die, which is 2,000. There is usually a challenge that revolves around the player obtaining some weapon in a stored location that requires the kit to access, so have that kit on!
You can replay any mission at any given time upon completion of the given mission. This achievement should be rather straightforward, so good luck hunting!
EDIT: According to a user, if you fail a Strike Force mission, a score of over 10k is still acceptable and counts toward the achievement.