The L-class destroyer is not a dreadnought/behemoth, it’s more like a sophisticated variant of the torpedo boat used frequently to destroy enemy dreadnoughts on maps such as Fao Fortress.
The L-class destroyer has 4 different seats, you can get progress towards the achievement with a kill from any of the seats, only 1 L-class destroyer can be deployed at 1 time.
The best way I found to get this achievement was to load up a conquest game on the Turning Tides DLC - Cape Helles, it will massively simplify things by using the server browser and filterering it to conquest only, choose the British Empire this is imperative as only the British Empire have access to the destroyer, now just wait, if there’s no destroyer available then there will be one deployed, simply wait until it has been destroyed or until you have an option to enter one of the seats, It usually takes a minute for a fresh destroyer to spawn, I would just spam down on the left analog stick to guarantee yourself a spot.
From here just simply kill 15 enemies, I’d recommend one of the cannons for efficiency, just try avoid the AA gun as they aren’t very effective for taking out infantry, make sure to spam RB when looking for enemies as it’ll spot enemies that you can’t see with the naked eye.
Thanks hope this helped!