One of the first things here is to use only the phrases you are already familiar with. If you chose a word or phrase that you're not sure about, you risk coming across as an amateur to your instructor, who is going to notice that right away when he or she reads it. Not all words that sound fancy fit properly in a sentence. What's more, the instructor would be suspicious whenever he comes across fancy and flamboyant sentences and phrases elsewhere in the essay. At the end, it's only your GPA and quality that's going to be impacted.
Secondly, don't lose your focus on the topic at hand. Your essay needs to be built around the research aims, as defined by its thesis statement. You have to resist the temptation of discussing issues that do not directly relate to the topic. Instead, make efforts to address examine and address all the minor or major points that link to the topic.
Going back to the topic at hand, how do you decide if you've engaged in critical thinking in your essay? The first thing about critical thinking is the ability to form independent judgements based on your own knowledge and experience. Instead of viewing any statement or argument in isolation, a critical thinker would present an opinion that takes into account a much broader perspective before making a claim.