IPA: /ˌiːɡəˈtɪstɪkli/
KK: /ɪˌɡoʊtɪsˈtɪkli/
In a way that shows excessive pride in oneself or one's achievements.
He spoke egotistically about his accomplishments, ignoring the contributions of his team.
Egotistically → It is formed from "ego" (from Latin, meaning I or self) and "-istically" (a suffix used to form adverbs indicating a manner or characteristic). The word describes behaving in a manner that is centered around oneself or self-interest.
Think of 'ego' as representing the self, and remember that 'egotistically' means acting in a way that focuses on oneself.