In the most direct sense, the narrator does not achieve anything tangible by the end of "In Dreams Begin Responsibilities." However, given the emotional intensity of the narrator's vision, he does achieve some insight into what to do and how he should live.
The premise of the story is one where little in the way of physical accomplishment is evident. The narrator watches footage of his mother's and father's courtship. It has already taken place with disastrous results. Nothing he can do can change that, and thus the narrator is not going to achieve anything of material value.
However, in this "dream" the narrator's own "responsibility" emerges. As the narrator watches the film, he recognizes the faults that were present from the very beginning. The narrator achieves the understanding that bad relationships don't just "happen." There are always telling signs. For example, the narrator notes how both of his parents lack a sense of wonderment: "The sun overhead does not disturb my father and my mother. They gaze idly at the ocean, scarcely interested in its harshness." The narrator sees this as a reflection of their inability to address all the challenges that will eventually face them. Another example is in the picture that is taken. Though it seems a harmless moment, the narrator notices the problems between them. These include the father's insistence that they "hurry up," the mother holding the bouquet in the wrong hand, and the photographer's impossible desire to make something beautiful. The narrator sees all of the relationship problems in this one instant: "...the picture is taken, with my father's smile turned to a grimace and my mother's bright and false. It takes a few minutes for the picture to be developed and as my parents sit in the curious light they become depressed." The narrator has recognized how this relationship was doomed to failure from the very start. Achieving this insight is what causes him to scream, "Don't do it! It's not too late to change your minds, both of you. Nothing good will come of it, only remorse, hatred, scandal, and two children whose characters are monstrous."
The narrator recognizes why his parents' marriage dissolved. He understands the importance of the signs that were there all along. When the narrator is eventually thrown out of the theatre, the usher speaks powerfully to him:
What are you doing? Don't you know you can't do things like this, you can't do whatever you want to do, even if other people aren't about? You will be sorry if you do not do what you should do. You can't carry on like this, it is not right, you will find that out soon enough, everything you do matters too much...
As the narrator wakes up from his dream, this knowledge is what lingers. He must carry himself with the responsibility that everything individuals do has meaning and does matter. The narrator recognizes that failure to see life in this way can lead to pain and hurt, as seen in the case of his parents. As he stands at the threshold of being an adult, the narrator has achieved two separate insights. The first is that he has learned how not to live. In watching the film, he has begun to understand what to avoid as he enters into longterm commitment and struggles with the emotional complexities that accompany age. The second is that what he does will have relevance and that his actions must be taken with this in mind.