失意泰然 is a very old Japanese proverb that suggests “keeping calm and collected at times of disappointment,” or “maintaining a serene state of mind when faced with adversity.”

It's hard to relate individual character meanings to the overall meaning unless you also understand Japanese grammar. The word order is very different than English. That being said, here's the character meaning breakdown:
失 To miss, lose or fail.
意 Feelings, thoughts, meaning.
泰 Safe, peaceful.
然 Like that, in that way, however, although.

Using these definitions in English, we might say, “Although you may fail or lose, have a feeling of peace and calm.”

失敗並非一種選擇 is probably the best way to say, “Failure is not an option,” in Chinese.

Just don't forget that some ancient Chinese proverbs suggest that failure is a learning opportunity that leads to success or innovation. So don't plan to fail but failure is only a waste if nothing is learned from the failure.

See Also:  Failure is a Stepping Stone to Success | Failure is the Mother of Success

義を見てせざるは勇なきなり is a Japanese proverb that means “Knowing what is right and not doing is a want of courage.”

I've also seen it translated as:
To see what is right, yet fail to do so, is a lack of courage.
To know righteousness, but take no action is cowardice.
You are a coward if you knew what was the right thing to do, but you did not take action.
Knowing what is right without practicing it betrays one's cowardice.

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

嘗試 is a close match for the English phrase “let us try” or the French word “Essayons.”

Essayons the motto of Combat Engineers in the U.S. Army.

This word can also be translated as “to try” or “to attempt.”

Even if you're not a Combat Engineer, this word should inspire you to attempt to accomplish difficult things. If you don't try, you are certain to fail; if you do try, at least there is a chance of success.

The worst thing is not failure, the worst thing is not trying at all.

This Japanese proverb can be translated as “flourish and wither, prosper and perish,” “life is full of fortune and misfortune,” or simply “vicissitudes of life.”

栄枯盛衰 / 榮枯盛衰 is about the rise and fall of human affairs or the ups and downs of life. Prosperity comes and goes, everything is fleeting and temporary, but like waves, another swell of prosperity may come.

Here's how the Kanji break down in this proverb:

栄 = prosper; thrive; flourish; boom.
枯 = wither; die.
盛 = prosperous; flourishing; thriving; successful; energetic; vigorous; enthusiastic.
衰 = become weaker; decline; get weak; die down; subside; abate; fail.

Notes: The original version of the first character looks like the image to the right. In modern Japan, they simplified that Kanji a bit into the version shown above. If you have a preference for which style is used for your calligraphy, please let me know when you place your order.

Apparently, with that original version of the first character, this is also used in Korean Hanja. However, I have not confirmed that it’s used in the same way or is widely-known in Korean.

七転八起 is a Japanese proverb that relays the vicissitudes of life, with the meaning “seven times down eight times up.”

Some would more naturally translate it into English as “Always rising after a fall or repeated failures” or compare it to the English, “If at first, you don't succeed, try, try again.”

The first Kanji is literally “7.” The second means “fall down” (sometimes this Kanji means “turn around,” “revolve” or “turn over” but in this case, it holds the meaning of “fall”). The third is “8.” And the last is “get up,” “rouse,” or “rise.”

Basically, if you fail 7 times, you should recover from those events and be prepared to rise an 8th time. This also applies if it is the world or circumstances that knock you down seven times...
...just remember that you have the ability to bounce back from any kind of adversity.

Note: This can be pronounced in two ways. One is “shichi ten hakki” or “shichitenhakki.” The other is “nana korobi ya oki” also written, “nanakorobi-yaoki.”

Special Note: The second character is a Kanji that is not used in China. Therefore, please select a Japanese calligrapher for this title.