For understand "One shot" you have to go back to his early discussion with his friends including Michael:
Michael: I'll tell ya one thing, if I found out my life had to end up in the mountains, it'd be all right, but it has to be in your mind.
Nick: What? One shot?
Michael: Two is pussy.
Nick: I don't think about one shot that much any more, Mike.
Michael: You have to think about one shot. One shot is what it's all about. The deer has to be taken with one shot. - wikiquote
That's why he said "One Shot" as that's what it takes to kill deer.
Michael: I came 12,000 miles back here to get you...What's the matter with you? Don't you recognize me?...Nicky, I love you, you're my friend. What are you doing? We don't have much time, Nick. [Nick pulls the trigger on a gun, clicking on an empty chamber] Is this what you want? Is this what you want? I love you, Nick. [Michael pulls the trigger, clicking on an empty chamber] Come on, Nicky, come home. Just come home. Home. Talk to me. [looking at Nick's track marks] What did you do to your arms? Do you remember the trees? Do you remember all the different ways of the trees? Do you remember that? Do you remember? Huh? The mountains? Do you remember all that?
Nick: One shot. [He smiles and laughs in recognition]
Michael: One shot, one shot.
[Nick pulls the trigger, shooting himself]
Michael: Nicky, Nicky, don't, Nick, no!!
So he did remember him in his last memories but he was so broke inside that he still killed himself. He was dead inside already.
Why he can't recognize him can be due to Dissociative Amnesia
Dissociative amnesia is a condition in which a person cannot remember important information about his or her life. This forgetting may be limited to certain specific areas (thematic), or may include much of the person’s life history and/or identity (general).
Dissociative amnesia has been linked to overwhelming stress, which may be caused by traumatic events such as war, abuse, accidents, or disasters. The person may have suffered the trauma or just witnessed it.
Or some other memory disorder but we can just guess as it was never explicitly told.