Tsuyoi in Chinese / Japanese...

強い means strong, potent, competent, domineering, tough, brawny, powerful, healthy, rugged, skilled, resilient, solid, or fierce.

This word is ambiguous without context, so it can mean any or all of these things if you wish.

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.

気の強い means strong-willed or strong of heart in Japanese.

Here's the character breakdown of this Japanese title:
気 (ki) spirit; mind; heart; nature; motivation; intention; feelings; essence.
の (no) possessive particle.
強い (tsuyoi) strong; powerful; mighty; potent; resistant; resilient; durable.

Note: Because this selection contains some special Japanese Hiragana characters, it should be written by a Japanese calligrapher.

強い体強い心 is a way to write “strong mind, strong body” in Japanese.

Each of the two lines starts with 強い (tsuyoi) which means: strong; powerful; mighty; potent; resistant; resilient; durable; tough; stiff; hard; inflexible.

The body is represented with 体 (the ancient version is 體, romanized as karada), which means: body; build; physique; posture; torso; trunk; health.

Mind is represented with 心 (kokoro), which can mean heart, mind, or soul, depending on context.

強い體強い心 is not a common phrase in Japanese, so it's not the most natural title for calligraphy. In English, you might want to write it, “strong mind, strong body” but, “strong mind, strong body,” is more natural in Japanese.

Note: Because this selection contains some special Japanese Hiragana characters, it should be written by a Japanese calligrapher.