Call of Duty: Black Ops II

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.

Finish the main campaign missions (non strike force) on veteran,
for sure u will get 10,000+ points each mission and then once you finish the game go back and replay the strike force missions on easy, the reason is, strike force on veteran is a pain in the ass, you can do it on whatever difficulty you want to but on easy its a cakewalk.

kill the majority of the enemies in each map and you will get 10k easy. took me around 30 mins to finish all strike force missions on easy.

Here's how I earned the Ten K achievement:
1. Set difficulty to "Recruit". Why not make the achievement easy?
General play-throughs should net you 10,000 points or more.
This step alone may earn you the achievement.

2. Strike Force missions are required for earning 10K, but "FOB Spectre" is not. I've 100% confirmed this fact. I earned 10,000+ points in all missions and the achievement did not pop until I completed the Strike Force missions. I still have 9,000-something points in "FOB Spectre", so that mission is NOT necessary.

3. If you somehow didn't earn 10,000 points on a mission (see your career record to see your score), try some easy challenges to add to your points. One easy challenge for all story missions is finding all 3 pieces of intel. Another easy story mission challenge is not dying in a mission (it's on Recruit difficulty, c'mon).

The "Second Chance" Strike Force mission contains an easy challenge of killing 10 enemies while playing as Chloe/Karma. "Odysseus" has 2 easy challenges of hitting 20 enemies with your Combatant Suppression Knuckles and finding Mason's personal items in his bunk at the very beginning of the level. The "Achilles' Veil" mission has an easy challenge for shooting the flying quad drones (I believe 20 of them).

All this will definitely get you the 10,000 needed if you didn't initially. See each video's YouTube page for author credit. An error won't let me manually label the videos with proper credits.