Jackals are a real nuisance on higher diffuculty modes. However almost any weapons works. The only diffuculty is their big energy shield.
One other problem. They usually come in groups of 3+. I like to use the battle rifle to fight them, but any accurate weapon will work. If you have grenades, hope that they are near a wall. If they are, throw it at the wall so that the grenade lands behind the fools. They will be blown up instantly.
Some of the best options are the Brute Shot, Fuel Rod Gun, and Rocket Launcher. A Jackals shield can deflect any small arms fire, but not the merciless barrage these explosived dish out.
Fire the FRG, or RL anywhere near the Jackals and they will die quite nicely. The Brute Shot has to be a little more accurate, since it has a smaller explosion. Just fire it at the Jackal and his shield will go down.
If you don't have these luxuries, you're going to have more of a challenge, albeit a small one. All you have to do is aim for the 'dent' in the jackals shield, which is where the fire their weapons from. If you hit there, the Jackals arm will be shot, and he'll be momentarily stunned. Use this to your advantage! Shoot that Jackal before he puts his shield up again!
But, if you're just too lazy, a couple melees will do just fine. 2-3 on easy and normal, and more on higher diffuculties.
Jackal snipers are another story. They are more of a nuisance than you could imagine. They can snipe your head off from halfway across the map on legendary, so they are your biggest threat. They use beam rifles, as well.
But, there is good news! They don't have shields!
All you have to do is shoot them in the head before they get you, and then you can go safely through. Also note that sometimes they can survive headshots with less powerful weapons, so make sure its down before you go past. And there is never just one. They usually have more than one sniper, except in a couple instances.