Halo 3

In the level where you spawn with a Spartan Laser (The Covenant), move forward until you destroy the Anti-Air Wraith. Save a few shots in your Splaser and just past where the Pelican drops off the Mongoose and Warthog, there will be a group of Banshees circling above. Keep moving towards them until one or two starts heading straight for you. You should have an even target and be able to take one down on the first try.

On the lower difficulties, don't even worry about dodging the Banshee's fire as you can withstand it. Just concentrate on hitting your target.

I got this achievement in the area on The Storm before the first Scarab, there is a missile pod at the top of one of the ramps (it's near the bottom of the right hand crane, as you look at the cranes), use that to take out any of the aircraft for this achievement

Start the level: The Storm. Now play untill you get to the space where the Scarab comes.quickly move to the bottem of the cranes where there are missile pods mounted. Look over the Horizon where you can see hornets and Banshees. Move your crosshair around that area untill it locks on to a banshee. Now fire a cupple of shots while its locked on. wait untill you see the banshee blow up. you should get the achievement. if not try it again. if the scarab comes the just let go of the pod and go destroy it, as it will block up your sights at the Banshees. once the scarab is gone try it again.

tip: If the scarab arives, take the lift up the crane. run to the end of the crane. wait untill the scarab us "close" to the crane then jump onto it. the you wont have to worry about taking out its legs.

OR you can Go into Multi-player and play the Map Valhalla. There is a banshee and a Spartan Lazer on this map so grab the Lazer (Splazer as some call it) and shoot the bird out of the sky.

Note: I suggest the first one over the second. As it can take a while to get the lazer, as because both teams rush for it.

soundskull bm's solution would be good, except that you don't spawn with the Spartan Laser if you load up from Rally Point Alpha, so...
Difficulty: Easy
Mission: The Covenant
Be sure you are Master Chief, so may want to do it alone.

Start out with a Spartan Laser and something else. DO NOT use any Splaser ammo or switch it out. Fly through the level as fast as you can killing whatever enemies you have to until you reach the part with the hornets. Now jump in one of them as the pilot and take off. In the distance to your right should be the first of a few "landing platform thingies" (viewable in video). Land, and most likely unless you are unlucky one of the enemy banshees has followed you. Quickly pull out and aim the Splaser and BAM! Achievement unlocked. If you miss, that is what the extra ammo you saved is for. If you don't get a Banshee to come within about 20m of you like I did first try or you run out of ammo you may want to revert to last checkpoint and try again. Eventualy you will get it I'm sure.