From the Main Menu, go to Play Online > Find Match > and then in that menu press
to switch to the Competitive playlists. Simply play ten matches in the same playlist and you will "place," earning you this achievement.
This Season is slightly different than before, so this achievement might pop under different circumstances. Before, the ranks reset and you had to re-place every Season. This time, ranks carry over. I can confirm that if you had Placement matches in progress (mine was 8/10 matches played), the achievement still unlocks when you place.
That being said, if anyone could confirm whether or not you get the achievement right away if you're already placed in every playlist, that would be great. Worst case scenario: If you are placed in every playlist and it turns out you
have to do placement matches for the achievement, simply not playing in that playlist for a while causes your Ranked progress to drop a bit. So it's possible if this is the case to just wait until your rank is dropped back into Unranked status.
EDITS:
According to Stig Assassin, if you have already placed in a playlist, completing one match in it should unlock the achievement.
I got the Achievement after one match in a playlist I was already ranked in.
According to MCFishHD, if you place and don't get the achievement, try playing one more match to completion.
if, like me, you never played ranked/competitive before, once you get your rank e.g Silver 2, you need to play one more game with that rank then at the end of THAT game your achievement will unlock.
According to metallicafan459, if it still isn't working...
performing a hard reset of the game and playing yet another match worked