The Gran has a long association with the underworld, particularly in the service of the Hutts. The most distinguishing feature is the three eye stalks on the head. The primary weapon of a Gran is the Thermal Detonator and over long distances this can be devastating. But in close range they'll switch to fists to avoid damaging themselves in a TD explosion.
Suggested Method of Attack - If the ceiling's low enough or you can duck through a door then a Gran will likely take itself out with TDs. But in large open areas you need to take them down before they can throw a TD. They have quite an arm, but it does have a limit; stay outside of it and pick them off with the Repeater or Bryar Pistol if you can. The Concussion Rifle is also good for med-long range attack. For medium range - if the Gran throws a TD, run TOWARDS THEM. This gives you a better chance of ducking under the detonator and avoiding the explosion, and also closes the distance so they can't throw any more. Once you get in close your shields are worthless, so either hit them with a fast weapon (Stormtrooper Rifle or Repeater) or switch to fists. Fists are probably the best if you can get your punches in quickly and keep away when they swing.