By fighter this does, in fact, mean ONLY the fighter which would be the planes that aren't flying straight lines and dropping bombs (bombers), making this achievement a bit more difficult to attain. You will first get rockets in mission 2, First Encounters at Midway, and they can be fired by pressing . They are direct fire, meaning they fire straight ahead and do not lock on to any targets, so your best bet is to lead your target well enough that the slow moving rocket will hit them and they'll blow up. If you can manage to get right behind an enemy, that's your best bet, but of course you can always fall back on the usually spray and pray and just fly through every level launching rockets nonstop (they're infinite, which will also get you the Trigger Happy achievement.
One way to get this a bit easier is to fly straight toward an enemy, as they LOVE to play chicken with you, giving you plenty of time to launch a few volleys of rockets at them, before veering off.