This is what Google Translate gives you, and it shows.

What a Japanese person actually thinks
Reads like a machine translated it — which is exactly what happened. The specific flavour is corporate training seminar: the same register as 顧客第一主義 ('customer-first-ism'). It's not funny, it's just flat and obviously foreign.

Meaning

Literally: soldier + spirit/mentality
Actually: Technically parseable as 'warrior mentality'. But no Japanese person has ever written this. It's two abstract nouns stacked because English put two words next to each other.

Scores

Naturalness●●●●●

Grammatical, and completely unused. This is the textbook example of translationese: every word correct, the whole thing wrong.

Coolness●●●●●

Zero. It has the visual density of a good kanji tattoo and the soul of a PowerPoint slide.

Watch out

high戦士 is closer to 'soldier' or a fantasy-RPG 'warrior' than to a samurai. Combined with 精神 it lands somewhere near 'combatant mindset'.

Get this instead

武士道 bushidō
the warrior's code

The real, established phrase for what you're reaching at.
闘魂 tōkon
fighting spirit

A real word, two characters, genuinely punchy. Famously Antonio Inoki's motto — so it reads as sincere fighting spirit, with a wrestling association.
不撓不屈 futō fukutsu
indomitable

If the meaning you want is 'I don't break', this is the established phrase.

On skin

戦士精神

Orientation: either

N/A — change the words.