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I, and a few others I've played, believe it to be tied with the amount of battles you've played and win percentage. From about Mercury to The Sun I was ranked as Legend (was on a hell of a winning streak), but then I started purposely going easy on the rookies and accidentally lost quite a few games due to sheer carelessness. That actually dropped me back down to Veteran for a while, so I assume it's win %.
I think I became a Veteran at about 50 total matches played. And I know that I became a Legend at exactly 100 total matches played. I have been a Legend ever since.
There are also other ranks. A few days ago when I was still a Rookie, I had a 30-0 win streak. After about ten wins I became a Bomber instead of Rookie, another ten matches later I became Rookie again and then I became Veteran (probably at 50 matches played). It was weird. I also played against a Soldier today, don't know how to get that one.