to fight bravely; make strenuous efforts — exerting oneself against difficulties or strong opponents; often used to praise effort or offer encouragement.
チームは健闘したが、決勝で惜しくも敗れた。
The team fought hard, but narrowly lost in the final.
受験生の皆さん、健闘を祈ります。
To all examinees — I wish you success in your efforts.
彼は最後まで健闘して勝ち残った。
He fought bravely until the end and made it through.