The word "berserker" today applies to anyone who fights with reckless abandon and disregard to even his own life, a concept used during the Vietnam War and in Vietnam-inspired literature (Michael Herr's Dispatches) and film (Oliver Stone's Platoon and Adrian Lyne's Jacob's Ladder). "Going berserk" in this context refers to an overdose of adrenaline-induced opioids (or military-issued amphetamine for long missions) in the human body and brain leading a soldier to fight with fearless rage and indifference, a state strikingly similar to that of the 9th century berserkers.
(Emphasis mine.)The important part here is indifference. Again, I find his behavior completely believable. It's not like the other guys were walking around in the open, everyone else was behind cover, and reacted appropriately when bullets were flying around. The number of bullets that are fired in real firefights, compared to how many actually hit a target, is much higher than we see in the movies. That so many could be fired and not hit him is not unbelievable to me. What was more unbelievable is that Martinez couldn't hit Rick as he ran across the bridge. Made a mess of the bridge but couldn't bring down the target, despite the fact that no one was firing at him to disrupt his aim.