The most dramatic point or moment would most likely be the moment of climax in the story line or play. The climax is the turning point in any story; the moment when the action or drama is at its highest point and the resolution comes into sight. Twelfth Night is composed of a few different plots, so there are a few different climaxes. One of the plots surrounds Viola's disguise and mistaken identity. Hence, the moment of climax surrounding that particular plot would be the moment when it looks like her true identity will be exposed at an inopportune moment.
Viola very nearly exposes her identity as a woman rather than as a male servant named Cesario when, at Fabian and Sir Toby's insistence, Sir Andrew challenges Viola as Cesario to a duel in Act 3, Scene 4. Naturally, since Viola is a woman, she has absolutely no education in the skill of sword fighting, and fearing for her life, tries to escape the situation. She's so terrified that she says she would "rather go with sir priest than sir knight" and that she doesn't care "who knows so much of [her] mettle" (III.iv.254-56). In other words, she is saying that she is more of a religious person than a fighter and does not care who knows of her cowardice. She even says she's about to confess her true identity as a woman in her aside, "Pray God defend me! A little thing would make me tell them how much I lack of a man" (282-83). Her identity is further nearly exposed when Antonio, the sea captain who rescued her brother, puts an end to the duel by offering to duel on Viola's behalf, whom he mistakes for Sebastian. This scene proves to be the climax because not only is her identity nearly exposed, leading to that part of the resolution, but also hearing Antonio call her by the name Sebastian makes her believe he is mistaking her for her brother, which gives her hope her brother is still alive, leading to yet further resolution. Since this is most definitely a climatic scene, it is also one of the most dramatic points in the play.