The literal translation of 'indomitable spirit' is:
I think it sounds okay, but if you have friends who are native Korean speakers,
try asking how the phrase sounds.
Both words are very abstract, and I just want you to have the perfect word with the exact nuance.
For example, there is a Korean word '투혼' which literally translates as 'fighting spirit'.
The translation sounds TERRIBLE, and no one would say that in western languages, but it is commonly used.
You can see that several translations of 'spirit' can exist, and a one-to-one translation may not do justice.
I think that the more opinions you can have from Korean speakers, the better.