You can take various approaches when writing an essay about sexism in advertising. Knowing that it is an essay gives you a good starting point. That is because knowing what type of essay you are supposed to write provides you with the structure of the essay, the goals of the essay, and the tone of the essay. In an analytical essay you need to bring critical thinking skills to discuss the topic. You could approach it as a question of history and show how the history of sexism meant that older advertisements were even more blatantly sexist than modern advertisements. You could discuss policy decisions that might lead to sexism in advertising. You could look at advertisements as art and do a critical analysis of one advertisement.
Some of the most graphic examples of misogyny and violence against women being an accepted part of American culture can be found in watch advertisements. The milder of these advertisements have focused on the trope that women are not on time. The more offensive of these ads have been surprisingly violent. There are old watch advertisements that feature crotch shots of bloody women, men seeming to strangle women, and other acts of violence.
However, these advertisements are having a surprising resurgence among watch manufacturers. Modern manufacturer Mariner is creating overtly sexist ads with the goal of creating a backlash against them in order to promote their products. These ads range from sexist tropes of a man surrounded by attractive women to an ad that clearly suggests a woman is being given some type of drug or alcohol against her will. This would be a fascinating series of ads to examine since they are intentionally sexist, in a way that is no longer considered acceptable, because the company wants to get that type of consumer.