It is when Captain Willard is in Nha Trang, being briefed on his impending mission, that he gets his first glimpse into the mindset of Colonel Walter E. Kurtz.  General Corman and Colonel Lucas are outlining the nature of Captain Willard's mission, along with a third man, a civilian, perhaps a CIA agent, known only as "Jerry", when the general requests that an audio tape be played for the captain, identifying it as an intercepted radio message out of Cambodia, confirmed to be the voice of Colonel Kurtz.

" I watched a snail crawl along the edge of a straight razor. That's my dream; that's my nightmare. Crawling, slithering, along the edge of a straight razor... and surviving."

Colonel Kurtz is making an abstract reference to the toughness and resilience of the North Vietnamese Communists.  He is alluding to the notion that the Vietcong are both willing and able to endure any amount of pain, suffering and torment in order to defeat the American forces in Vietnam.  They will never give up no matter how much napalm is dropped on them, no matter if their towns and villages are destroyed, no matter how much death is inflicted upon them.  It is this kind of toughness and resilience that is in effect Kurtz's dream in that he is trying to duplicate it among his montagnard soldiers out in his Cambodian outpost.  But on the other hand, it is his nightmare in that these are already the traits of his enemy, an enemy that he knows is highly skilled and motivated, an enemy that is willing to fight to the last man, woman, and child.