More than a Handful - Kill 125 enemies in multiplayer Matchmaking - 2500cR
Simple enough, kill a bunch of dudes. This'll probably add a few to your multikills too. Grifball or Multi-Team for some speed, other than that, play how you want.
Flat Tire - Kill 10 enemy vehicles in Firefight Matchmaking - 2343cR
Again? Well, yeah. Firefight Limited works well, usually get a bunch of Vehicles but it's harder than your regular Firefight, I'd say Arcadefight on a large map through Firefight Doubles.
...Is a Virtue - Score 60,000 points in any Campaign mission with less than 3 deaths - 4500cR
Patience is not what's needed here. Long Night of Solace from Rally Point Alpha with as many skulls on as possible and as hard as possible. Then, blow shit up.
Sweep the Leg - Perform an Assassination in a multiplayer Matchmaking game - 2000cR
Speed, Stealth and Height, get one and then jump on someone and assassinate them. Objective games work best due to the disadvantage of the objective holder (Speed, lack of motion tracker)