"On one uppers" is a colloquial term often used to describe people who constantly try to outdo others or make themselves seem better. There are several phrases that can be used as synonyms to describe such individuals. One is "braggers," which implies someone who is constantly bragging about their achievements. Another is "show-offs," which suggests someone who is eager to show off their skills or talents. "Attention seekers" is another term for individuals who crave attention and will go to great lengths to receive it. Finally, "domineering" describes a person who is controlling or overbearing in their interactions with others. These terms all accurately describe the behavior of "on one uppers".