Taekwon-do was described by the founder as 'a way of life' but you need to be able to understand the tenets in order to follow them. Here I will attempt to explain the difference between perseverance and indomitable spirit.

Perseverance / In Nae
Steady persistence in adhering to a course of action, a belief, or a purpose; steadfastness. To continue to (try to) do something in spite of difficulties, failure or opposition. - This implies that things are taking longer than expected, there are ostacles to overcome, whether physical or mental. For example, you get stuck on a particular grade or technique yet carry on trying, you fail a grading but pick yourself up determine to improve and try again, you are continually beaten in competitions yet never give up entering them, that is perseverance.

And in life... patience in pursuing your goals whatever they are. ”One who is impatient in trivial matters can seldom achieve success in matters of great importance.” (Confucius)

Indomitable Spirit / Baekjul Boolgul
Indomitable - 'Incapable of being overcome, subdued, or vanquished; unconquerable.' (www.thefreedictionary.com). Impossible to defeat or subdue. - This implies that someone or something is trying to defeat you.

"It is an act of cowardice to fail to speak out against injustice." (Confucius) "All that is necessary for evil to triumph is for good men to do nothing" (Edmund Burke)

Indomitable spirit means you stand up for what you believe is right no matter what. Don't wait for it to be someone else's fight.

It seems to me that you can't have indomitable spirit without having perseverance, but you can have perseverance without having indomitable spirit. Indomitable spirit is like the ultimate perseverance. Whilst perseverance is to carry on trying and trying for something despite difficulties or failures, indomitable spirit is to carry on trying and trying in the face of (almost) impossible odds and adversity because you know its the right thing to do.