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REA

The 1000 headshots (helicopters) title does NOT exist. I thought it did because it exists in MW2 and the headshot/multi-kill challenge is replaced with helicopters. HOWEVER, the 2500 gun kills title is available for the Stinger at 2000 vehicles taken down, which is very rare

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DROP ZONE.
In drop zone, you can usually get 15-30 vehicles down per game. It doesn't seem like much, but just spend a few games or so doing it and you're already 100/2000!
Just shoot down the care package carriers. Aim a stinger at the spot it's going to be, and fire when it locks on. Blind Eye PRO helps a lot.
Also, the enemies still get killstreaks from the crates, and you can shoot those down. If they call in strafe run, lock on to he helicopter in the middle and fire for 3 helicopter kills.
I'm currently 500/2000 vehicles using this method. I would suggest doing about 250-300 per prestige. This way you should get most of the challenges from Blind Eye, stinger, etc, for the most xp.