“变得自高自大”可以翻译为“become arrogant” 或者 “grow conceited” 。例如：
After achieving some success, he became arrogant. （在取得一些成功后，他变得自高自大了。）
Don't grow conceited just because you've done well in this exam. （不要仅仅因为这次考试考得好就变得自高自大。）