To be competitive, you need good test scores (consistent with being able to pass the boards). You not passing the boards, and maybe not getting a job, will become our problem. It's a problem fellowships don't want.
You also need to have extra elective time in the specialty (showing significant interest).
Research is a big plus. Maybe not a requirement, but remember that most Fellowship programs are at places that place significant value on academic productivity and have some research requirement. A history of some academic interest will make you a better fit.
And most importantly, you need better than average letters of recommendation ideally from people in that specialty.
That will get you an interview.👍
Then you need to sell yourself hard and seem like a good fit for the department. If you're arrogant, odd, can't articulate you interest and career goals, etc. you're not getting a spot. You have to kill the interview.
I get the sense that things are getting more competitive across the board, if you want a competitive fellowship (desirable area, highly regarded program, etc) you need to plan ahead and bring your A game.
I'm not a big believer that fellowships are a requirement for the future, but if your skill set includes things that most CRNAs realistically won't want to/be able to do alone, your job is more secure. It's also certainly possible that in the future a gov't system might pay some more for additional required time in training. Who knows? Having said that, I don't believe that's it's worth the loss of a year of income for a fellowship unless you're passionate about that subspecialty.
Good luck.