In Halo 1, Jackals only carried plasma pistols, but as you can see from this shot, in Halo 2 they wield other weapons, including plasma rifles and possibly even needlers.

The armband shields they carry are not as effective as the full body shields used by Elites, but they will deflect most projectile weapons and are even good against plasma rifles.

The best strategies against Jackals are to try and shoot areas unprotected by the shield, which are easier to hit when they are in motion, or to use the alt-fire of a plasma pistol to drain the shield and then switch to another weapon while it cools.

Like the Elite's shields, a drained Jackal shield will recharge over time. Jackals with drained shields, like Elites, will also often retreat and take cover while their shields recharge.

Grenades can be effective against Jackals, especially when used behind them where their shields do not protect.

The Halo 2 manual refers to Jackals as "excellent shots" and indicates they have higher status than Grunts.