I don't think their life has to include so much a tragic aspect as...

1) They simply have to have gone up against "the man" in some way (record execs, the government, etc).

2) Either that, or their eccentrics/personality kept them from being able to live a normal life / connect with people important to them, etc. Which, yeah, would technically fit under the "tragic" umbrella, I guess.

3) And then there's the "process" biopic that's basically about how whatever brilliant artist created whatever seminal record/sound.

For instance, Love & Mercy - the Brian Wilson movie - fits the last two criteria.

Then, there's no tragic aspect in something like A Complete Unknown. In fact, Bob Dylan basically shows up to New York one day and is instantly so good, the red carpet is rolled out for him almost immediately, and he basically becomes famous overnight. The tension/drama then comes from A) him having to choose between Elle Fanning and Monica Barboro in his personal life, and B) him "going electric" when the "folk" gatekeepers want him to stay in his/their lane in his professional life.

I'm sure there other criteria I'm forgetting, but those are the main ones that stick out to me.