Answer:
The lines are indeed " Hope is the thing with feathers That perches in the soul"
Step-by-step explanation:
A metaphor is a figure of speech that compares two different things in order to attribute a quality of one of them to the other. To make such comparison, the metaphor states that "thing A is thing B". Dickinson uses this figure of speech to compare hope to a bird, a feeling to an animal. The literal meaning would make no sense, but we can grasp that she is trying to attribute some quality belonging to a bird to the feeling of hope - maybe its lightness.
Note: A simile is a figure of speech similar to a metaphor in the sense that it also makes a comparison. It needs support words that the metaphor doesn't use - "as" or "like". Let's make it clear that a metaphor does not use the words "like" or "as".