Willard (Martin Sheen)’s Timeline and Summary

Willard, waiting for his next mission, gets drunk in his hotel room and has a little breakdown. He cuts his hand when punching a mirror. He's a sweaty, disgusting mess.
Next day, he meets with his commanding officers, who order him to assassinate a rogue soldier, Colonel Kurtz, running a private army in Cambodia. He accepts the mission.
He journeys down the coast on a boat to a place where a group of Air Cavalry helicopters, led by Colonel Kilgore, agree to escort him to the mouth of the river they'll be journeying down.
An intense helicopter battle ensues, but they make it to the river.
During the journey, Willard acts mainly as an observer, except for when he shoots an already injured Vietnamese woman.
After two members of the crew die and they come under attack from Kurtz's army, they finally arrive at Kurtz's Cambodian compound.
After talking with Willard and getting philosophical, Kurtz imprisons him, beheads Chef, and helpfully dumps the head in Willard's lap.
Then he lets Willard go. Kurtz knows Willard came to kill him. He wants to die.
Willard hacks Kurtz to death and keeps walking back to the boat when it's clear that the tribespeople seem to consider him their new leader.
He switches off the boat's radio and heads downriver.