The way I would understand this sentence were it using しても (instead of してでも) is:
More literal translation: Even (しても) sacrificing my own spirit and life, the status quo won't do!
Idiomatic translation: Even if it's at my own expense, I can't let things continue like this!
My best guess is that してでも means "even if it's the case (で) that I do", whereas しても means just "even if I do". So the extra で is kind of like んだ at the end of a sentence ("it's the case that..").
NOTE: I've seen other questions on this site which attempt to explain the difference between ても and てでも, but I found them hard to understand and I thought discussing it in the context of this new sentence might be useful.