Everyone I’ve talked to has a vague idea but not specifics. I got into Silver league even though I never once beat the boss on the scoreboard or after clicking submit. The highest rank I got was 70th. So how does it really work? Apologies if this is answered elsewhere; 
if so a link would be awesome.
You need to be ranked over the boss.
Every 4 min, all of those that are ranked over “Boss” will ascend to Silver.
Every 1h, all of those that are ranked over “Robossnik” will ascend to Gold.
You may have not beaten it first, but your AI still battle it and eventually, you were ranking above the “Boss”.
Fear not, it’s far more difficult to beat Robossnik
There is no link yet. The league concept is still in test.
A tutorial and a blog post will be released soon to explain what it is.
@hack in fact you’re right. There is a delay (about 20seconds) between the match computing and the stabilization of the rank. So, if you look at the rank when matches are 100% finished, your rank is not exact.
We are aware of this, and will provide a better feedback soon to be sure that your rank is fully calculated.
First of all, thank you very much for introducing leagues, I think they add a lot more excitement to this contest with the bots too. We are already aware of how promotions from bronze and silver happen, however we don’t know how one will be promoted from gold to legend, and if there will be any new rules/modes in legend, or is it just a distinction from gold? Any information regarding these would be much appreciated. Thank you!
I also have been very much enjoying the league aspect of this contest but…
I have been trying to beat Robossnik (leader of Silver league) for a couple of days now, and have been “Oh so close!” for most of the day today. Then, all of a sudden, I got a notification that I would be promoted to gold about 15 minutes ago. I was surprised, so I went to look at the leader board, and… Robossnik is no longer in the Silver league!!! Now there’s a bot called NegaBoss in the league, and he’s ranked way the heck down at 307.
Did you re-jigger the difficulty level in mid-contest? I’m confused. 
As you could read at https://www.codingame.com/blog/en/2016/05/bot-programming-challenges-get-polished.html, the difficulty curve has been tweaked, as (presumably) too many players got stuck at silver. It wouldn’t change how the final ranking will look, but it is indeed a bit disappointing. 