You must obtain the three vehicle warfare ribbons for the achievement. Listed below are the vehicle types in ech category for you.
Air Warfare Ribbon is obtained by killing 6 enemies in a single round with any of the following vehicles:
Jets: F/A 18 Super Hornet, A10 Thunderbolt, Sukhoi Su-35 (SU-35BM FLANKER-E), Sukhoi Su-39 (SU-25TM FROGFOOT)
Helicopters: AH-1Z Viper, Z-11W, AH-6J Little Bird, MI - 28 Havoc.
@ darthluigi7 has pointed out, getting kills from the door gunner of transport heli's as confirmed so far such as KA - 60 Kasatka, UH- 1Y Venom will net transport warfare ribbons and not the intended Air Warfare. I'm not sure if this was intentional or something that may need to be patched but for now Air Warfare ribbons will need to be earned as a pilot or a gunner manning nose mounted turret/secondary weaponry but not side mounted machine guns on the transport choppers.
Transport Warfare Ribbon is obtained by killing 4 enemies in a single round with any combination of the following vehicles:
Transport:Humvee, Vodnik, Growler ITV, VDV Buggy, RHIB Boat, AAV-7A1 / Amphibious Assault V.
Door Gunner KA - 60 Kasatka, UH- 1Y
Armoured Warfare Ribbon is obtained by killing 7 enemies with any combination of the following vehicles:
LAV: LAV-25, BMP-2, 9K22 Tunguska, LAV-AD, Bradley Fighting Vehicle, BMD-3
Tanks: M1 Abrams, T-90
To help the longevity of your aircraft/vehicle ensure you're a engineer with the repair tool and as you rank with the vehicles the difficulty to staying alive and notching the kills will decrease as upgrades like smoke, flares and guided missiles are invaluable.
If possible make attempts for these ribbons with squad mates or team members in vehicles that have multiple seats. Two, three or more people repairing and spotting hostiles is a lot better for your life expectancy than trying to lone wolf it.
Air Warfare will give most people the trouble, the way I was able to obtain was finding a decent pilot so you can enter the gunner seat in a bird like the Viper. We only focused on providing air support for our squads capturing flags below in conquest, flares were a huge help and so was the stealth upgrade from the gun seat. If we were damaged he'd fly away from the action and land if nec. were we could repair. If we did go down we wait in the squad spawn menu until the chopper respawned.