This achievement is glitched in a good way.I expect this to always work, as it has gone unchanged for over two years and dozens of patches.This is currently unlocking after you play only ONE league match. Yay!
And no, I do not mean retroactively because I already met the requirements. I have only played one Leagues game ever (also note -- "League" matches aren't actually called that anymore; the name was changed to simply "Ranked" a long time ago). It does not matter what type (Duel, Conquest, Joust). You must be level 30 to play ranked, meaning you have obtained this achievement:
If you're not level 30, you will not be allowed to queue ranked (it is a requirement of the game).
I played a Ranked Duel and it unlocked immediately.
Let me know if this does not work for you (as that would mean it has been patched), and I will update the solution.
Thank you to MAC10million for being the one to show me this, I just wanted to spread the word.