This achievement is very misleading and I have yet to see a guide that gives the correct information.
First off, it is not as simple as just casually destroying six gunships during your playthrough of Half-Life 2. Turns out there are only six which you can actually destroy.
Gunships are flying vehicles of the Combine. They are smaller than dropships and shoot at you a lot more. Try not to mix them up. The most effective weapon to take down gunships is the rocket launcher. It takes three or four good hits to destroy the gunships. Your rockets can also be shot down if you're not careful. A good method is to shoot your rockets and spiral them around the gunship until it hits.
That being said, the first gunship you can destroy for this achievement is in Chapter 7: Highway 17. You will have to stop your buggy for a gate in the village of Little Odessa. Immediately after receiving the launcher a gunship will begin attacking the small town. Make your way to the top floor of the building. There is a hole in the wall for you to shoot the gunship through and a wooden box with three more rockets set on top.
The next gunship will come after you use the crane to lift your buggy up on to the high platform. Once you drive your buggy up and around on to the next highway the gunship will start attacking you. Continue on the highway until you reach the road block of piled-up cars. In the middle of this traffic jam is a destroyed van with a box of unlimited rockets inside.
Near the end of this chapter you will encounter the third gunship. After working your way across the underside of the bridge to disable the barriers, a gunship will disturb you on your way back. The very middle house has a nice cache of rockets waiting for you.
The last three gunships appear during the next chapter, Sandtraps. About one-third of the way into the chapter you'll have to park your buggy in a garage. Immediately after, dropships will bring in groups of Combine solderis. Once you deal with all four dropships, make your way to the top of the lighthouse. There is an unlimited box of rockets on the top floor and a gunship as soon as you get on the roof.
The final gunships come when you are working your way into Nova Prospekt. After battling past the guard towers and the bottom row of offices, the box of unlimited rockets is on a raised platform behind the first building. Close to where you enter the prison.
There are three other gunships that appear in Half-Life 2. One in Chapter 11: Follow Freeman, but it will fly away before you can destroy it. Two more spawn at the very end of the game if you take too long. These can be destroyed but will NOT count towards the achievement.
One final thing to note is that this achievement does not carry between saves. You must get all six gunships in one playthrough. This will spare you some time and frustration, as i missed this achievement my first time through, not knowing there were only six gunships.