"胜任各项工作" can be translated into English as "be competent in all tasks" or "be capable of handling various tasks".
Here are some example sentences for context:
With his extensive experience and skills, he is competent in all tasks assigned to him.
(凭借他丰富的经验和技能,他能够胜任交给他的各项工作。)
She has proven herself to be capable of handling various tasks efficiently and effectively.
(她已经证明了自己能够高效且有效地完成各项工作。)