PART 1 (I have made a few additions, mainly link-words)

In this presentation, we have to highlight the fact that Cleopatra's beauty and power are exceptional if not supernatural. Our work is divided in two parts, one about Cleopatra’s influence and the other about Cleopatra's beauty.

First, as far as her beauty is concerned, lines 8-9: "the barge she sat in like a burnished throne burned on the water" is a metaphor showing how radiant Cleopatra's boat was and also how everything she was in contact with had to be extremely beautiful. "Burned on the water" is an oxymoron: fire cannot resist water and it also shows how supernatural her boat was. The impossible becomes possible.
Line 10-11, when the speaker says that "the sails [were] so perfumed that the winds were lovesick with them" the reader may perceive two meanings. On the one hand you can say that it is an allegory to show how her incredible scent invaded the air. Or on the other hand you can say that, in fact, the winds represent the gods that came all the way down to see her and were astonished by her beauty. On top of things, it seems Cleopatra directly affects the state of natural elements.
In the same way, lines 25-26 tell us that "her gentlewomen” are like “so many mermaids" and that "a seeming mermaid steers" We can see that even the mermaids, magical creatures, known for their incredible beauty, came to see Cleopatra and admire her and her perfection. That not only means that she is more beautiful than the mermaids, but also that magical creatures take their orders from her. 
Line 32-33 the reader is told that "the city cast her people upon her" This is a personification that shows that even the city, an inanimate object, came to see her, which is obviously impossible but that means that she really does have a supernatural influence/aura. She gives life to lifeless things. Incidentally, the verb “cast” is a clear reference to the lexical field of spells and bewitching, an allusion to her influence on Antony. As a matter of fact, through lines 3-4+39-45, one can see that Antony has deeply fallen in love with Cleopatra as if she had cast a spell on him ("she pursed up his heart on the river of Cydnus"). The fact that she says no to Antony' invitation to supper and that he seems to accept it shows how strong her influence is on him, she manages to bend the will of one of Rome’s most powerful leaders, which is quite something for the queen of a supposedly inferior kingdom that was to become a Roman province.

Concerning Cleopatra's beauty, line 5: "there she appeared" reflects that she did not just arrive like a normal being, no she appeared like a goddess, out of nowhere, as if she was an angel with a golden aura around her that made everyone astonished by her arrival.
The unsuccessful attempt of the speaker at describing her beauty "for her own person it beggared all description" line 15 is a hyperbole. Her perfection cannot be put into words because such words don’t exist and any attempt would not be enough = would be of no avail. That reminds us once more that she is or is like a goddess, human words are helpless when it comes to portray her. 
Line 1, the expression "a most triumphant lady" summarizes what she reflected on the day she met Antony. It shows her as a victorious lady, someone so powerful that no one can compete against her. And as we said earlier on, that is a reversal of the roles and of the usually accepted balance of powers because, at that time the Roman Empire was the most powerful whereas in the play, it's Cleopatra who plays this role.
To conclude we can say that, even the great Shakespeare could not describe Cleopatra with simple words and that he was forced to use a lot of figures of speech.

Ludmila (with Yoen, Noe & Alina)