Like all Phantoms, Adam endured many injuries. It was a constant part of every mission and battle he went on. If a Phantom wasn't getting wounded, then he wasn't fighting or moving forward.
Adam was alive, so none of the wounds proved fatal.
However, several times the situation was on the verge between life and death. Phantoms had strong bodies and high stamina, they could withstand dozens of cuts and bruises. Blood loss was important, but not as critical as for an ordinary human.
The same was true for the Phantom organs. The energy helped them survive the most crises.
Sure, without a heart or brain, a Phantom would not be able to continue fighting, but those were the only two critical points.
So if a Phantom was in the middle of a battle, the worst injury he could receive was the loss of one of his limbs.
