It's raining plasma
This hovering purple mortar tank shouldn't be much of a threat as long as you keep mobile or use cover well, and keep an eye on where those giant plasma balls are heading. However, when you're simultaneously engaged with other aggressors, things can become a bit more tricky. Also, Marines are pretty clueless about keeping clear of the incoming blasts, and are likely to get quickly blown into next Sunday unless you take it out quick.
A few rockets will take care of it, as would a Warthog gunner whilst you zip around at a reasonable distance to avoid the slow and clumsy fire. Strafing it with a Ghost is another option if you're confident with that; you can quite safely circle it while firing (there's an example of circle-strafing in BCM56 at 0:11). Of course, you can also take it out from the air with a Banshee, though you have to be careful. You can also destroy it with small arms fire and grenades, but it'll take a while. Note also that unlike the Ghost, you can destroy a Wraith whilst it's unmanned.
If you fancy something a bit more gladiatorial, bear in mind that you can use a Banshee to get under a manned Wraith and flip it over, causing the pilot to be amusingly ejected. It's not too hard after a bit of practice. You can do it by ramming the front fast and low to get the nose up, then pushing it up and over, though this follow-up phase can often become quite a messy tussle and it may soon be better to break off for a fresh approach. The Wraith can of course blast you as you approach, but you can help avoid that by waiting for a shot before you charge in. For that to work, you need to be fairly close so it's unlikely to have time to get a second shot off. You could execute a slow orbiting path, then when the shot fires, curve in quick.
One other flipping tip. If there are any Marines around to distract the pilot, you can get a chance to ram the Wraith from the rear low down, with spectacular effect! Under normal circumstances you're unlikely to get such a chance as the pilot is quick to sense you and turn to face you.
Against Banshee and Scorpion blasts and small arms fire, the Wraith seems to have the same resilience all over (e.g. on Heroic it takes 87 pistol rounds to destroy, no matter what part you aim at). Against rockets and plasma grenades though, it has weak spots worth going for, as follows.
In regard to a rocket blast, the turret area is weakest. The blast damage comes with a degree of randomization, but on average you'll do around 80% more damage there compared to hitting the nose. The dark side area is weak too. On Heroic it's mostly as weak as the turret area, but on the other difficulty levels it seems marginally stronger than that. The rear part of the dark side area (behind the back fin) is stronger than the rest. It seems to have a similar degree of weakness to both the front and back fins, where a hit does around 20% more damage than on the nose. Unexpectedly, the rear is as strong as the nose.
The main practical upshot of all that is that if you pick out the turret or side, it'll usually take you one fewer rockets to destroy the Wraith; or potentially two fewer on Legendary (it would normally take four on Legendary, three on Heroic or Normal, and two on Easy).
As for plasma grenades, the weak spots look like being similar to those for rockets. A plasma grenade to the turret or unarmoured side seems to cause around 25% more damage than one to the nose.
Note: If you want to know how you can test this sort of stuff, see my related HBO forum post.
Sadly, you can't get into this monster yourself. What, seat the wrong size or something? Aw nuts!