The barbarian was left out of the gun-using archetypes in UC. Some of you made attempts to integrate the Cleric and the Alchemist, so I'll try this instead.
Here to you...
Shooting Fury: At 2nd level, a lethal weapon gains the Amateur Gunslinger feat, and can use any 1st-level Gunslinger deed. At every four levels thereafter, the lethal weapon may choose a Gunslinger deed of his level or lower in place of a rage power. This replaces uncanny dodge.
Gritty Rage: The lethal weapon can fuel his rage spending grit points. 1 grit point expended grants him an additional round of rage. This replaces improved uncanny dodge.
Rage Deeds: The lethal weapon has access to the following rage powers:
Dislodge Joint: When raging, the barbarian can dislodge his own joints as a standard action to break free from a grapple or a bond, ignoring the pain (he doesn't take damage immediately). The lethal weapon gains a bonus equal to his barbarian level to one Escape Artist check. He can't move the dislodged limb but otherwise fights normally. He must relodge the joint at the end of the rage with a mighty blow, suffering all the pain and damage he would have taken before and being fatigued for 1d6 rounds more. This power may be used just once for rage.
Mad Machinegun: While raging, the lethal weapon can spend 2 grit points to make an additional attack with a firearm in a round.
I think that "barbarians" can be found in every age and society. Rambo is a Barbarian. And definitely Martin Riggs is a barbarian with a gun (and Fast Movement indeed!)^^
P. S. I forgot:
The rage powers which complement the lethal weapon archetype are: Auspicious Mark, Bestial Leaper, Boasting Taunt, Brawler, Chaos Totem, Come and Get Me, Greater Brawler, Lesser Chaos Totem, No Escape, Raging Leaper, Reckless Abandon, Roused Anger, Sprint, Strenght Surge, Swift Foot, Unexpected Strike.
Some little changes and here's the final result. The interaction with Terrifying Howl seemed too tasty to let it go^^. Moreover, I reintroduced medium armor but gave up the free firearm proficiency at 1st level, following the trophy hunter archetype- after all, a barbarian comes (at least as 1st level) from a non-firearm-using culture, so it's reasonable that he must take the proficiency spending a feat on his own. I moved the Shooting Fury ability at 1st level not to make him receive both a rage power and a deed at the same point.
Gritty Rage: The lethal weapon can fuel his rage spending grit points. 1 grit point expended grants him an additional round of rage. This replaces improved uncanny dodge.
Rage Deeds: The lethal weapon has access to the following rage powers:
Dislodge Joint: When raging, the barbarian can dislodge his own joints as a standard action to break free from a grapple or a bond, ignoring the pain (he doesn't take damage immediately). The lethal weapon gains a bonus equal to his barbarian level to one Escape Artist check. He can't move the dislodged limb but otherwise fights normally. He must relodge the joint at the end of the rage with a mighty blow, suffering all the pain and damage he would have taken before and being fatigued for 1d6 rounds more. This power may be used just once for rage.
Mad Machinegun: While raging, the lethal weapon can spend 2 grit points to make an additional attack with a firearm in a round.
Rage Powers: The rage powers which complement the lethal weapon archetype are: Auspicious Mark, Bestial Leaper, Boasting Taunt, Brawler, Chaos Totem, Come and Get Me, Greater Brawler, Intimidating Glare, Lesser Chaos Totem, No Escape, Raging Leaper, Reckless Abandon, Roused Anger, Sprint, Strenght Surge, Swift Foot, Terrifying Howl, Unexpected Strike.