The phrase in Engpsh to express "努力尽力" is "do one's best".
This phrase originates from the Engpsh idiom "give it one's best shot", which means to try as hard as one can to achieve something. "Do one's best" is a simppfied form of the idiom and is commonly used to express the idea of putting in a maximum effort.
Example 1: "I will do my best to finish the project on time." (我会努力尽力完成项目。)
Example 2: "She always does her best in everything she does." (她总是尽力去做她所做的事情。)