Perform as well as one can; do the utmost possible. Also 'do one's level best' or 'do one's damnedest.'
Examples:
- I'm doing my best to balance this statement.
- She did her level best to pass the course.
Origin: First term from 16th century; 'level best' from mid-1800s.
Synonyms: do one, , , s damnedest