Cardinal Richelieu is the country’s top statesman. He knows it, everybody else knows it, and even the King knows it. Unfortunately it’s still not quite enough to get him the girl. Queen Anne rejected his advances a while ago, and he’s been fuming about it ever since.
He’s cut off all her support and planted spies among her attendants in the hopes of catching her doing something she shouldn’t—like giving the Duke of Buckingham some valuable diamond studs that originally came from her husband:
Richelieu, as everyone knows, had loved the queen. Was this love a simple political affair, or was it naturally one of those profound passions, which Anne of Austria inspired in those who approached her? That we are not able to say; but at all events, we have seen, by the anterior developments of this story, that Buckingham had the advantage over him, and in two or three circumstances, particularly that of the diamond studs, had, thanks to the devotedness of the three musketeers and the courage and conduct of D’Artagnan, cruelly mystified him.
It was, then, Richelieu’s object, not only to get rid of an enemy of France, but to avenge himself on a rival; but this vengeance must be grand and striking and worthy in every way of a man who held in his hand, as his weapon for combat, the forces of a kingdom. (41.10 – 41.11)
In the novel, he's credited with having almost supernatural powers of detection and prevention. At one point our heroes ask one of the lackeys to eat (yes, actually eat) a sensitive letter because they fear Richelieu has invented a means of reading ashes (yes, actually reading ashes).
His power is absolutely great, and although he is the main antagonist in the novel, it’s clear that he respects loyalty, courage, and military ability. He can’t understand why D’Artagnan would be a royalist instead of a cardinalist, and tries to woo him with a promotion. By the end of the novel, the two men are on cordial terms and it’s clear that they don’t have much to fear from each other. This evidence argues in favor of placing the title of "Big Bad" onto the character of Milady.
In real life, Cardinal Richelieu was indeed a superb statesman, famed for centralizing power in France and remaining a staunch opponent to the growing power of Austria and Spain. It is highly unlikely that Richelieu was ever in love with Queen Anne, but he did make her life very difficult since she was a foreigner and he suspected her of aiding her countrymen against France.