Enlisted

The achievement means 100 tanks and airctafts combined. I believe your best bet is to focus on destroying tanks. Destroying empty enemy tanks also counts. Here are some ways to destroy tanks that I know of, according to how far I progressed in the campaign so far:

- "Explosion Packs". Some soldiers from some squads come pre-equipped with them. You can get more to equip more soldiers with them by spending "Orders for weaponry" on them in the Logistics tab, Equipment Delivery. You need 2 bronze orders for weaponry to get 1 Explosion Pack. You obtain orders for weaponry by completing battle tasks, achievements, challenges and from battle pass rewards, all of which are displayed in and accessed from the main menu in the Soldiers tab. You must throw the Explosion Packs directly onto a tank, or under it or to its sides. It must explode really close to the tank otherwise it won't get destroyed. It might sound silly, but as it is really, really easy to miss the throw, I leave my other soldiers from my squad behind by ordering them to defend a place (double-tap X), then I sneak up on the enemy tank and when I'm close I hold RT to cook the Explosion Pack until the game automatically throws it at the tank and it explodes immediately after, giving the enemy tankers no time to move away, usually killing my soldier too, so it's a bit of a kamikaze tactic, but it works well
P.S. Regular fragmentation grenades sometimes work too if the tank is already damaged enough, but to a much lesser extent than explosion packs.
P.P.S. For more explosion goodness you can carry two explosion packs/grenades with you if you equip a "Grenade Pouch" on your soldier. The grenade pouch can be obtained for one bronze order for weaponry from Logistics, Equipment delivery. You must first unlock the "Backpack slot" upgrade for the respective class from Upgrades, Personnel upgrades.

- "AT Stationary Guns". This method is more involved as you need an "Engineer" squad and you need to unlock the AT Stationary Gun upgrade for that squad from the Upgrades tab, Squad Upgrades. You need Squad Points to unlock upgrades and you earn those by leveling up your squad as a whole. You level up your squad by playing with it, getting kills and capturing objectives. Once you have that upgrade, in the match, playing as an Engineer in that squad, you switch to the "Construction Hammer" (comes equipped by default and is unequipable) by pressing Y, you hold d-pad left which brings up the constructions radial menu and you press RB to select the AT stationary gun. Then you look for a suitable place to build it (where it glows green) and start holding RT to construct it. Once built, you get in it by pressing X shortly. When you aim at a tank you should look for the aiming reticle to turn green. That means your shot will penetrate the tank and you'll do damage. The AT stationary gun leaves you very vulnerable and it's really fragile, so it won't work too well if the enemy tank reacts fast.

- The anti-tank weapons. They have the bomber class icon next to their name. For example in the Battle for Moscow campaign on the Axis side you have the "PzB-38" and "PzB 39". When you get a new bomber squad the main bomber soldier will come equipped with an anti-tank weapon by default as his specialty weapon, so you get one for free. This weapons fires single strong armor piercing shots and is best used from a moderate distance behind cover. You should aim roughly at the weak spots of the enemy tank, such as the engine or the ammo rack, to the sides and the back of the tank. You can also aim at the tracks to destroy them and render the tank immobile. You can also kill the tankers inside if you visualize where they are positioned (roughly the center of the tank) and get lucky with your shots.

- Tank to tank combat. Unfortunately I can't give specifics on this, because I consider tank to tank combat utterly atrocious in this game. Every time I tried it, it was a waste of time, couldn't penetrate any shots and we just keep shooting at each other for a minute until eventually my tank blows up somehow.

You can also try your luck at knocking down some airctafts:

- You can damage airctafts with your guns. Just aim ahead of them as they get close to the ground when they do their strafing/bombing runs and hope you damage them a little. If the pilot decides to bail or crash shortly after, you get credit for destroying that airctaft.

- "AAA Stationary Guns". Again with the Engineer squad; there is a squad upgrade for AAA stationary guns. You use the Engineer's Construction Hammer to build the AAA stationary gun, hop in it and try to shoot at the enemy airctaft. A little marker appears ahead of the airctaft and that's where you should aim the AAA stationary gun. Considering how fast airctafts move, you probably won't hit it too well, but maybe you get lucky

- Dogfighting. No clue about this, never tried it. I find the airctaft piloting controls horrendous. Theoretically you would get behind the enemy airctaft and shoot ahead of it (a little marker appears) with your machine guns.

That's about all I know in terms of methods to destroy tanks and airctafts so far. I will add more to this guide as I make more progress in the campaign and unlock more stuff. Feel free to share in the comments more ways to destroy tanks or airctafts and I will add them to my solution and credit you.

These are updated methods to grind them in a custom games with friends:

Custom match settings;
Game mode: squads
Difficulty: Standard
Max AI soldiers: 2, so bots wont spawn when you have at least 2 players in the match
Team armies: mixed
A Password
Only map/mission is Airfield West (Allies)

The red team will being the attacking team on this map and will be one getting the vehicles kills because the defenders have infinite lives. For the red team, I recommend using the first tank you start out of in Allies Berlin for the cannon is pretty good if you don't have any late game tanks unlocked. Blue team will be the ones being grinded and I recommend the use of the starting tank for Axis Normandy (Nickname: "Puma") for they are fast and have ammo spots in the front which make them pretty easy to one shot. Tanks have a 2.5 minute cool down after spawning in to be used again and you also need to die as two different squads after your tank to be able use it again too. You can kill your soldiers by holding the select button and pushing "Kill the soldier" and I recommend to make your infantry squads small as possible to make this process quicker.

The red team can pretty much spawn camp the tank spawn for the defenders by going past the objective on the right side and sticking to the road until the grey zone which the defenders can spawn and run straight out in front of the attacker team. Pumas are very weak and can even be killed with HE ammo to the front where the ammo is stored right above the front wheels. There are ammo resupplies at your tank spawn if you run out of ammo. This will be more efficient if you have someone with multiple tank squads but that requires a campaign grinded to have more tank squads and money spent of the game for premium which allows you an extra vehicle slot and the ability to buy more slots permanently.

Another possible way to grind these vehicles kills are through the bombing raid ability that Radio man squads can unlock now which spawns in 5 bombers that count as airctafts kills. This does require you be decent at using airctafts and I recommend the Normandy Axis BF 110 you get at level 4 due to the sheer about of firepower it has at a earlier level in a campaign and should shred bombers pretty easily. These raids can have a very long cooldown, especially without the cooldown squad perk for the radio squad.

The airfield map does have biplanes sitting around on the runway and they could count as airctafts kills but I've never tested so I don't know if its possible.

I also think you need to finish the match to get credit for the kills as well so keep that in mind.