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打たれ強い is often used as a martial arts term.
It means being able to take a lot of punishment or being able to take a hit. In Japanese baseball, it can also refer to the pitcher's ability to keep his cool when the batter gets a hit. 打たれ強い is generally about being resilient and strong in the face of criticism or adversity.
Note: Because this selection contains some special Japanese Hiragana characters, it should be written by a Japanese calligrapher.