What does Helena hope to achieve by telling Demetrius of Lysander and Hermia's flight in A Midsummer Night's Dream?
Helena tells Demetrius that Hermia and Lysander have run away because she hopes that he will change his mind and fall for her.
A Midsummer Night’s Dream is a simple story, really. Hermia and Lysander and are in love, but her father would rather she be in love with someone else—Demetrius. That’s an old story. This does not please Helena either, because she is also in love with Demetrius. She would just as soon leave Hermia to Lysander. Hermia is her friend anyway.
When Hermia’s father does not relent, Hermia and Lysander decide to run away, and Hermia makes the unwise choice to tell her friend Helena. When Helena is chasing after Demetrius, trying everything she can to get him to stay, he is not having any of it. He wants to marry Hermia. After all, her father is the Duke of Athens. If he pairs up with Hermia, that’s a match where he’s going somewhere!
Helena decides to use the one chip she’s got, since her pleading and her feminine wiles are not getting her anywhere. This is why, almost as soon as Hermia tells Helena her plans, she turns around and has a soliloquy about Demetrius in which she vows to tell him.
I will go tell him of fair Hermia's flight;
Then to the wood will he tomorrow night
Pursue her; and for this intelligence
If I have thanks, it is a dear expense. (Act 1, Scene 1)
Note also that Helena is quite angry at this point. She feels spurned by Demetrius, because he loved her. In fact, Lysander testifies to the fact before Egeus. Helena is hot-headed, and at the point where she makes this speech she is hot indeed. She notes that upon one look from Hermia his love for her “dissolv'd.” You can hardly blame her, in a way.
Of course, we need Helena to tell Demetrius about the lovers’ flight, from a dramatic standpoint, because she is the one who sets the story in motion. Her jealousy gets the ball rolling. It sends everyone into the woods. Demetrius follows Hermia, Helena follows Demetrius, and chaos ensues.