The phrase "show oneself off" refers to acting in a way that draws attention, often with the intention of impressing others. There are various synonyms that can be used depending on the context. For example, "showboating" means to show off one's skills or abilities in an ostentatious or excessive manner. "Flaunting" suggests displaying something with the intention of provoking envy or admiration. "Exhibiting" can be used to describe presenting oneself or one's talents in a public setting. "Posturing" implies an artificial or exaggerated display of confidence or superiority. Finally, "grandstanding" refers to actions or speeches intended to impress or gain attention from others.