You don't need any specific boomstick to destroy a helicopter, but there are two boomsticks which are extremely good at this job, let's start with our second place

This fully-automatic 12.7x108mm bad boy does have some really big rounds, basically all you need to do is shoot somewhere around a helicopter until it's down

pros:
- easy to use
- does a lot of damage
- infinite ammo (50 rounds per belt)
- can be used on distances up to 1km
cons:
- mounted on a tripod, can be used only while placed
- can only be picked up
- often bugs and just doesn't respawn when destroyed

The best of the best, at least in a good hands, often used as anti-infantry weapon

pros:
- oneshots everything
- meme gun
- comes with RPG class and can be picked up from dead teammate
- cool rocket sounds
- handheld anti-air
- can kill with it's backblast
cons:
- there are none

After you chose your personal anti-helicopter weapon, you can start your duck hunting, i will provide some protips on how to efficiently destroy any annoying birds in the sky

step 1: find a helicopter
step 2: wait for a good moment
step 3: try to kill the pilots
If failed, repeat steps 2 and 3 until helicopter is destroyed

step 1: find and grab the dshk before your teammates (hardest step)
step 2: find a good spot where you can see the sky
step 3: wait for the helicopters to appear
step 4: just aim at the general direction of a helicopter and shoot at it
pro tip: avoid cobras

step 1: grab an RPG class
step 1.1: steal an RPG from dead teammate (skip if step 1 was successful)
step 2: find a helicopter
step 3: wait for a good moment
step 4: just erase enemy helicopter with your left mouse button
pro tip: crouch helps with aiming
pro tip 2: don't kill your teammates with backblast (or just pretend that this was an accident)

Now you know how to absolutely annihilate helicopters, just keep your eyes open and no pilot will be able to get away from his inevitable death, good luck, fellow hunter