Any advice on this front?
If you're going for CTO of SpaceX, yes, you'll need some overwhelming accomplishments. If you're going for developer role 437 at SpaceX, less so :)
[1] when compared to peers, e.g the people going for the same jobs as you
[2] and will definitely prefer a nice 'average' person, to an obnoxious 'genius'
I'll take it further: It doesn't even need to be your _biggest_ accomplishment! For example, you can choose to talk about _the first_ time you did something, say, lead a small project from start to finish with some result X. Then you explain why you're so proud of that accomplishment: Because previously you only worked on projects led by others, or only took over existing projects, etc, but this was the first time you managed a project from planning all the way through release and support. That means it was the first time you faced challenges such as X, Y, and Z, and you overcame them by doing this and that...
And although you've led many other bigger and more interesting projects since then, this one small project made you a better leader and better engineer, and that's why you consider it one of your greatest personal accomplishments.
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Notice how in an answer like this you get to throw in all sorts of things that hiring managers love: Challenges you've faced, how you overcame them, how you approach problems, leadership experience, how you think, etc.
And by the way, the great thing about "greatest" is that it's relative, so there's no wrong answer. Some times it's better to tell of a smaller accomplishment if there's a better story that goes along with it.