I don´t remember right now how, but I managed to kill him at third or fourth attempt. So it is possible just get the gun and ALL ammunition. Maybe you ran out of it too early? Look around, there is another box. I think you just did not pick up all ammo. I think there is no secret beyond this; after killing Hitler you see the credits and greetings to the Lynx fans.
EDIT Have looked it up:
108stars has played through it on Youtube, have a look:
Right before meeting and shooting the evil dictator, from 11:35 on, the player in the video has 48 HP and 11 bullets.
First you empty your handgun on him, then you have to PASS him to the left and enter that room there, because in there is the machine gun and more ammo