Ah, this is where it gets interesting, the problem with propaganda is it quite contains elements of truth mixed in with hyperbole and fiction. Making it more difficult still is the general lack of surviving literature that is propaganda produced during the Final War of the Roman Republic. However it is possible to separate some truths from inventions and embellishments, and the political literature and histories produced after the fact can be a huge aid to revealing what some of the main accusations leveled against Cleopatra were. However it is worth noting that they were all written roughly a century or more after the fact. First I am going to outline some common themes, then look at the historical basis (or lack thereof) for some of them, before looking at why they might have been selected and repeated from a cultural and literary perspective.

One of the most obvious claims was that Cleopatra had designs on Rome itself and sought to gain dominion over it. An overarching theme of her megalomaniacal designs nots just over Egypt, Asia and those Eastern territories of Africa, but over the world itself Roman History by Cassius Dio echoes this fear when recounting her alleged intention to seduce Octavian where he states

Consequently she expected to gain not only forgiveness and the sovereignty over the Egyptians, but the empire of the Romans as well.

and further, when reflecting upon her life and death

Cleopatra was of insatiable passion and insatiable avarice; she was swayed often by laudable ambition, but often by overweening effrontery. By love she gained the title of Queen of the Egyptians, and when she hoped by the same means to win also that of Queen of the Romans, she failed of this and lost the other besides. She captivated the two greatest Romans of her day, and because of the third she destroyed herself.

But perhaps the speech Dio attributes to Octavian is the best example of Roman patriotic sentiments in the war

For that we who are Romans and lords of the greatest and best portion of the world should be despised and trodden under foot by an Egyptian woman is unworthy of our fathers, who overthrew Pyrrhus, Philip, Perseus, and Antiochus, who drove the Numantians and the Carthaginians from their homes, who cut down the Cimbri and the Ambrones; it is unworthy also of ourselves, who have subjugated the Gauls, subdued the Pannonians, advanced as far as the Ister, crossed the Rhine, and passed over the sea into Britain. Would not all those who have performed the exploits I have named grieve mightily if they should learn that we had succumbed to an accursed woman? Should we not be acting most disgracefully if, after surpassing all men everywhere in valour, we should then meekly bear the insults of this throng, 6 who, oh heavens! are Alexandrians and Egyptians (what worse or what truer name could one apply to them?), who worship reptiles and beasts as gods, who embalm their own bodies to give them the semblance of immortality, who are most reckless in effrontery but most feeble in courage, and who, worst of all, are slaves to a woman and not to a man, and yet have dared to lay claim to our possessions and to use us to help them acquire them, expecting that we will voluntarily give up to them the prosperity which we possess?

The poet Horace in his Odes also alludes to this

Twas shame to broach, before today, The Caecuban, while Egypt's dame Threaten'd our power in dust to lay And wrap the Capitol in flame,

And Lucan repeats this in the historical poem Pharsalia in which he calls her

Egypt's shame; Fury of Latium; to the bane of Rome Unchaste. For as the Spartan queen of yore By fatal beauty Argos urged to strife And Ilium's homes, so Cleopatra roused Italia's frenzy. By her drum she called Down on the Capitol terror (if to speak Such word be lawful); mixed with Roman arms Coward Canopus, hoping she might lead A Pharian triumph, Caesar in her train; And 'twas in doubt upon Leucadian waves Whether a woman, not of Roman blood, Should hold the world in awe. Such lofty thoughts Seized on her soul upon that night in which The wanton daughter of Pellean kings First shared our leaders' couches. Who shall blame Antonius for the madness of his love, When Caesar's haughty breast drew in the flame? Who red with carnage, 'mid the clash of arms, In palace haunted by Pompeius' shade, Gave place to love; and in adulterous bed, Magnus forgotten, from the Queen impure, To Julia gave a brother: on the bounds Of furthest Libya permitting thus His foe to gather: while in dalliance base He waited on his mistress, and to her Pharos would give; for her would conquer all.

In all of these she is shown as having used her seductive charms first to manipulate Julius Caesar into giving her Egypt and then to bend Antony to her will in order to dominate Rome. Far from being a war of aggression, Rome's opposition to Cleopatra is portrayed as a self defensive action, and Antony is a willing traitor duped into siding with a foreign queen over his own country. This is a very important thing for Augustean propaganda to emphasise because it shifts the focus away from Augustus being the victor of yet another civil war against a fellow Roman supported by a client-king (er, queen) and paints a much prettier picture of him triumphing over an Egyptian schemer and love-slave of a Roman. There is also just the slightest touch of apologia over Julius Caesar's actions.

The Jewish historian Josephus follows in this tradition but his writings are perhaps not to be viewed as direct continuation of Roman propaganda, but deriving from Herod's enmity with Cleopatra and Josephus' own reliance on the accounts of one Nicolaus of Damascus. In Antiquities of the Jews, he very openly derides her character and criticises her activity in political affairs as well as emphasising her sway over Antony.

Now at this time the affairs of Syria were in confusion by Cleopatra's constant persuasions to Antony to make an attempt upon every body's dominions; for she persuaded him to take those dominions away from their several princes, and bestow them upon her; and she had a mighty influence upon him, by reason of his being enslaved to her by his affections. She was also by nature very covetous, and stuck at no wickedness.

And again he speaks of the

covetous humor of this wicked creature: yet did not all this suffice so extravagant a woman, who was a slave to her lusts, but she still imagined that she wanted every thing she could think of, and did her utmost to gain it; for which reason she hurried Antony on perpetually to deprive others of their dominions, and give them to her. And as she went over Syria with him, she contrived to get it into her possession; so he slew Lysanias, the son of Ptolemy, accusing him of his bringing the Parthians upon those countries. She also petitioned Antony to give her Judea and Arabia; and, in order thereto, desired him to take these countries away from their present governors. As for Antony, he was so entirely overcome by this woman, that one would not think her conversation only could do it, but that he was some way or other bewitched to do whatsoever she would have him; yet did the grossest parts of her injustice make him so ashamed, that he would not always hearken to her to do those flagrant enormities she would have persuaded him to. That therefore he might not totally deny her, nor, by doing every thing which she enjoined him, appear openly to be an ill man

So again, the common theme of a power hungry seductress and the implication, or outright statement, of her unnatural greed and/or lust. Interestingly, Josephus gives an account not present in other histories of Cleopatra's attempt to seduce or otherwise mislead Herod of Judea for her own gains only to be outmaneuvered by him which is similar to Dio's story of her attempt to seduce Octavian or at least move him to pity.

More generally, accusations of her amorality, promiscuity, avarice, decadence, and occasionally, drunkenness were thrown around. This is an important part of Lucan's characterisation of Cleopatra's court as an exotic, decadent place of befuddling luxuries,

When she had purchased at so vast a price Peace from the chief, the joys of such a peace A feast proclaimed. There in full pomp the Queen Displayed her luxuries, as yet unknown To Roman manners.

This ties back into Cleopatra's role as a covetous seducer

Upon either hand Lay kings, and Caesar in the midst supreme. There in her fatal beauty lay the Queen Thick daubed with unguents, nor with throne content Nor with her brother spouse; laden she lay On neck and hair with all the Red Sea spoils, And faint beneath the weight of gems and gold.

Horace is savage af about depicting the often invoked image of of Cleopatra's feminized decadent court yet again and implying her own personal weakness.

Girt with her foul emasculate throng, By Fortune's sweet new wine befool'd, In hope's ungovern'd weakness strong To hope for all; but soon she cool'd, To see one ship from burning 'scape; Great Caesar taught her dizzy brain, Made mad by Mareotic grape, To feel the sobering truth of pain,

And of course, the ever important accusations of her use of potions or other sorceries to bewitch Caesar and Antony. Lucan has Pothinus, tutor to Ptolemy XIII state this in regards to Caesar

By amorous potions she has won the man

Josephus brings it up but does not assign much certainty to it necessarily,

As for Antony, he was so entirely overcome by this woman, that one would not think her conversation only could do it, but that he was some way or other bewitched to do whatsoever she would have him;

Tl;Dr Cleopatra is a promiscuous, greedy, amoral, manipulative tyrant who wants to destroy Rome and has probably been planning this treachery from the start which is why she turned one of our greatest leaders into her lackey.

I am short on space but I will expand on this below.