As with all of Bungie's Covenant baddies, the character work for the Jackal is utterly superb. The way he skulks about, the way he points and rolls, the way he comically retreats with shield over head, the way he emits a low growl (hackles rising) when sensing that you're nearby somewhere, the way he sometimes recoils in delayed shock on seeing a grenade at his feet or a 7ft cyborg standing next to him. And then there's his hilarious agonized reaction when you land a plasma grenade on him or fill him full of needles, making it all the more satisfying to do so. It's things like this that really add to the experience. Top marks to the Bungie folk for their brilliant and thoughtful character design.
Two types of ugly
Jackals seem to come in two flavours. Brown-skinned ones with yellow shields, and green-skinned ones with blue shields. But if there's any fighting difference between them, I can't say I've noticed. They carry the plasma pistol and make full use of its overcharge feature. Their normal fire can be extremely rapid on the higher difficulty levels.
Plasma ball threat
Plasma balls from Jackals are perhaps your second biggest threat after Elites with plasma rifles. Your shield is wiped in one go, and if there's more enemy firing you'll start to lose health fast. So, keep alert for the humming sound of a Jackal's overcharging pistol, and for its approaching green glow; you know he's ready to let you have it in the face.
Also listen out for released plasma balls when enemies are on multiple sides. You can hear the direction and dodge accordingly, even if you're not looking (such as when pistol sniping in another direction). With enough practice, this should become something you do instinctively. You can get lots of practice in the Far area defence for the rockslide megabattle, in which enemies close in on you across a wide front.
In open ground Jackals sometimes send in plasma balls from extremely long range, which can take you by surprise if busy with enemies closer to hand, as you can easily miss the release sound, if it's even audible at all. These fiendishly accurate shots will still wipe your shield of course, so beware. Just because he's crouched behind his shield miles away doesn't mean he's no threat. This is something you'll encounter regularly in the rockslide megabattle for example.
Plasma ball bonus
Plasma balls aren't always bad news though. As they're often fired from the rear of the enemy ranks, it's not uncommon for one to hit an Elite in the back, taking down his shield. You could even try to encourage that with suitable positioning and movement. When you see it happen, you'll have a nice opening for finishing off the Elite quick - e.g. with pistol fire. It's especially something you're likely to see quite often in megabattles, where the covies are quite thick on the ground.
Pistol against Jackal
The pistol is especially good for sniping a Jackal at medium to long distance. Quite often he'll point viciously on spotting you, giving you a great opportunity to take him down there and then, or at least to interrupt him with a quick shot to the hide. When he's moving towards you, you can exploit the rhythm of his step by timing your shots for when the fleshy area is largest. When he rolls to the side, you've got a brief opportunity for a headshot before he gets up; or you can just pile shots into his body. And when he turns tail and runs for it with his shield over his head, it's open season.
Exploiting the roll
Importantly, when a Jackal is sitting firm behind his shield, don't think you have to bring down his shield to get at him. Try loosing off a shot, and quite often he'll fire back and roll. The roll is your cue to give him some hurt, as some unprotected flesh is briefly in view. Of course, there's also the option of aiming for his exposed weapon hand as he crouches. If you manage to make him flinch, it opens the door to further shots.
When you're relatively close to a Jackal and he rolls (perhaps prompted by your pinging a shot off his shield), it's fairly easy to tag him with a plasma grenade to his exposed back as he starts to get up. The moment he's tagged, you know he won't be troubling you any more! This can be a useful tactic in pressured situations, when it's important to switch attention to other threats as quickly as possible.
Getting through his shield
If you want to get through a Jackal's shield, the quick way is to hit it with a plasma ball from a plasma pistol. The slow way is to wear it down with a plasma weapon; but it takes so long that you could be forgiven for not knowing you could do it at all, and it would surely be better to just shoot for his exposed hand.
When you're one-on-one with a Jackal and you have a plasma pistol, I recommend moving in with a plasma ball to remove his shield and stun him, then giving him a satisfying whack or two. I don't know about you, but of all the enemies the Jackal is the one I most like to hand out a good whacking to, the skulking beak-nosed freaks! If you want to be even more gratuitously vindictive (yes please), follow your plasma ball by tagging him with a plasma grenade while he's still stunned, and watch his amusing reaction. It's one of my favourite tactics, particularly when mopping up in the rockslide megabattle. If he runs back among his mates, so much the better.
You might have thought the needler useless against Jackals from the front, having seen the needles bounce off their shields. But it's actually not that difficult to send Jackals up in beautiful pink clouds from a near-frontal angle. The best way is to exploit the homing behaviour of the needles. If you fire needles while circling left, the needles will arc in and bury into his side, now exposed to them because he's rotated to keep facing you. When a bunch of needles embed and an explosion is imminent, the Jackal's agonized reaction is wonderful to behold.
If you don't want to leave cover, you can just fire anyway. Quite often he'll fire and roll, leaving himself briefly vulnerable to any incoming needles. Even if only a few get through, there's a good chance he'll start to skulk away, shield over head, in which case you've got a free target.
You can also do the following, when relatively far away. As he crouches behind his shield, send in a stream. Just as it's nearing him, ping a shot off his shield with another weapon. This makes him roll, during which time the needles arrive and pile in. Bye-bye beak-face!
When you've got Marines in support, try flanking a Jackal so his shield can't cover all the angles of incoming fire.
Finish him off
When a Jackal's shield goes down, it takes quite a while to eventually go back up. Naturally, you should hunt down the skulking beastie before that happens, if you have the opportunity.