You can use a mix of challenges and missions for this achievement. To unlock challenges, try doing a lot of stars in the missions.
I found the race challenges easiest: I did them all on 3 star rating. Also, the first few gun challenges are easy, but sniper, RPG and machinegun are some of the hardest challenges. Don't bother with Hotswap, unless you want to go for the 20 max rating achievement.
On top of my head, here are a few missions that you'll want to try for this achievement:
Start shooting from the parachute. From up there, blow up the barrels when soldiers and the vehicle come near. You should get a 9X multiplier easily. After that, don't die too much and use the tank to blow up the vehicles for extra score. Try downing 1 or 2 helicopters at the end.
Same map as mission 1. You'll want to get a good multiplier in the first 2 parts of the mission. Use a Rifleman and learn where the enemies spawn in the first wave (or at least use your radar). Move back and forth to these spawn points and check the roofs for RPGs. Use the mounted gun (truck) when a vehicle arrives at the end of the 1st wave. Use the same tactic in the 2nd wave. In the 3rd wave, you'll want to blow up the truck and helicopter for extra points.
Mission 3 - snipers.
They always spawn at the same place. So it's only a matter of learning the spawn points, and quickly taking them out. 5 snipers in the first building area, then 4 parachuting in the snowy area, then 3 snipers on a rooftop. After the second helicopter and parachuting squad, you have a couple enemies on the ground near a truck. Keep your multiplier running and you'll be fine. If you're missing an enemy to finish the mission, he's always on the ground, so jump down and quickly kill him.
Mission 4. Submerged.
(At the start, hit Y to drop from your parachute and then hit it again to pull it back). Take out all enemies in front of the 1st bunker and get a x9. Quickly blow up the bunker and get another decent multiplier from the wave with a truck (stay there as long as enemies come, you have enough time anyway). Then it's a matter of advancing through the 2nd bunker area and the entrance of the pier without taking too much casualties. Take out the submarines and rush the end when you get enough points.
Mission Burning Bridges.
I did it in 2:30!! But it's hard: you'll want a good mission start. Take the sniper and quickly kill the machinegunner in the helo before he takes down your squad. If you're fast, you can then switch to a SpecOps and run though the mission with a single man. This will give you boosts (quick reload, etc) and enough points to complete the mission