In Hamlet, the image of women is one of dependence upon male chivalry and solicitude.
Through characterization, we can learn about a character directly or indirectly. Direct characterization allows the author or narrator to tell us about a character's personality or nature. On the other hand, in indirect characterization, we learn about characters by observing their speech, speech patterns, behavior, idiosyncrasies, habits, and thoughts before forming our opinions about them.
In literature, imagery is textual description that appeals to the five senses; a writer uses imagery to paint a particular image of a character or the main theme. In Hamlet, the image of women is one of subservience and docility. Shakespeare also portrays women as pawns in a masculine universe. Even as queen, Gertrude herself has no personal agency and no autonomy in matters of the state. After her husband's death, she finds herself in a precarious situation.
If she rejects Claudius' suit, both she and Hamlet will find themselves without a home. There can only be one queen, and Gertrude must make sure that she's the one sitting next to Claudius on his throne. A younger queen will likely bear Claudius a new heir, which will leave Hamlet politically and materially disadvantaged. So, by every indication, Gertrude marries Claudius as a matter of convenience as well as survival. Yet, Hamlet, grieved beyond measure by the death of his father, thinks differently about his mother's actions. He thinks that she's actuated by lust, a very unfair judgment on his part.
Here, the image of femininity is one of disloyalty and fickleness. Women are portrayed as having very little devotion; yet, without true personal autonomy, a woman in Shakespeare's time had very little recourse to justice or consideration. She was at the mercy of masculine inclinations and laws.
In the play, Claudius is the chief power player after his brother's death. He orders Gertrude to spy on Hamlet and uses Ophelia to discover what the young prince is thinking. In Act 3, Scene 1, it is clear that both Gertrude and Ophelia have allowed themselves to be used as pawns in Claudius and Polonius' schemes. Gertrude tells Ophelia that she hopes the young girl is the real source of Hamlet's angst, and Ophelia agrees.
When Ophelia tries to return to the young prince what she claims are gifts and love letters from him, Hamlet denounces her. He ends up accusing her of being a whore and castigating her for being a deceptive beauty:
Be thou as chaste as ice, as pure as snow, thou shalt not escape calumny...I have heard of your paintings too, well enough. God has given you one face and you make yourselves another. You jig and amble, and you lisp, you nickname God’s creatures and make your wantonness your ignorance. (Act 3, Scene 1)
Basically, Ophelia is used crudely and mercilessly by the men in her life. On the one hand, her father (Polonius) and Claudius use her as bait to entrap Hamlet. On the other hand, she is denigrated and verbally abused by Hamlet for doing Polonius and King Claudius' bidding. In the play, Ophelia actually harbors romantic feelings towards Hamlet, but she's not even allowed a word in edgewise due to Hamlet's hostility. So, in the play, women are portrayed as persecuted, passive, and docile creatures; their image is one of utter dependence upon the whims of men.