Banshee
I'll have one in yellow please
Now we're talking! Personally I'm really looking forward to the future when Bungie has achieved its commendable plan of world domination, and everybody has been issued their own personal Banshee to whoosh around in. Great fun.
Ground targets
When taking out ground targets, you have a couple of options. For maximum safety you can hover a long way off and send in bolts from the fuel rod cannon (perhaps switching to the plasma cannon whilst recharging, if close enough). You may need to move occasionally if a Wraith shot looks threatening. Also beware of Grunts with fuel rod guns; I've underestimated those little devils more often than I care to admit! If you want to feel closer to the action yet still be relatively safe, you can swoop around in tight loops, sending in a bolt each time around. But on Legendary in particular, you really don't want to be low enough to come under fire from ground troops, notably Elites with plasma rifles. Those things hurt!
When using the hovering approach, I generally use thrust-firing to improve my targeting, particularly when a long way off. Just make a brief forwards motion each time you fire, to make the shot straighter and faster. Of course, when using the low tight loop approach, you're automatically using thrust-firing. If a Jackal's plasma ball is heading for you as you hover, you can simply let yourself freefall slightly so the shot goes over the top. The same goes for Hunter blasts and Wraith shots, if you care to hold your nerve.
In tackling a collection of enemy, preferably take out any Shades first as they have the range to damage you. To minimize the amount of fire you take, fly around them until you're ready to send in a shot from the fuel rod cannon. Their fire will usually lag well behind you. Briefly dive in to release the shot, then back out.
Vertical descent
Did you know that the 'A' button causes you to descend vertically? You can potentially use that for landing, though personally I tend to just swoop in.
If you want to lose a lot of altitude quickly, powerless free-falling seems to be faster than doing a power dive. Once you get low enough, hit the power and pull out of the fall.
Anti-Banshee tactics
On foot, the easiest way to take out a Banshee is with a pistol. On Heroic it takes something like 15 shots, causing Elite ejection in just a few seconds. Maybe use the zoomed view when it's far off. Maybe use automatic fire when it's not veering about too much. When it dives in on an attacking run, preferably take cover before your shield starts bleeping, then pop back out and resume firing as it veers off and away.
I quite enjoy taking it down with an assault rifle too. If you want to be efficient with your ammo, wait for it to dive towards you, then fire rapid bursts as it comes in and swoops off. You can bring it down on its first run if you get it right. If you don't mind being more wasteful with ammo, you can also pepper it as it flies about further away. Plenty of bullets will miss, but the few that hit will all add to the damage.
The plasma rifle and plasma pistol can also be used. Actually, it's a nice challenge to see how quickly you can do the job with these weapons in combination. You can do the most damage when it's heading straight for you. Rapid shots from the plasma pistol would do nicely there; pile them into the nose until forced to duck back under cover. When it veers off, you could switch to the plasma rifle and try to continue getting hits, which is where your skill in leading the target and anticipating course changes can make a big difference. Or you could send a 'chaser shot' after it; a plasma ball that chases after the Banshee and homes in, though the pilot may veer away before it catches up. It's great fun delivering the final blow to a smoking Banshee that way. The pilot thinks he's getting away, then the chaser finally catches up and BOOM! Comical stuff, and very satisfying. A chaser shot is best fired when the Banshee is still very close to you and preferably flying almost directly away. I often make a brief run to line myself up behind it as best I can, then send the shot off using thrust-firing.
You can even tag a Banshee with a plasma grenade. Takes practice, but it's pretty satisfying when you manage it. Perhaps try a long throw as it's heading in; or brave the plasma heading your way and wait until it's much closer up.
To use the rocket launcher, you'd best let the Banshee come in on a run. Once it's heading straight for you, let fly, possibly using the zoomed-in view so you can get it further away. But don't move away too soon, else the Banshee may veer off before getting hit. You may take a bit of fire, but hopefully not enough to matter. Rocketing a Banshee when travelling across your line of sight is rather hard even at short range, but you may like to try it just for the challenge. It should be pretty satisfying if you manage to connect.
If you've got a Warthog handy, the chain-gun is likely to make pretty short work of a Banshee of course. If you use it yourself though, you run the risk of getting blasted with a Banshee bolt if you let it come in on a diving run. It would be safer to let a Marine man the gun while you drive around evasively.
For some concentrated anti-Banshee combat, see Banshee battle engineering. Good fun and great practice.