To get to 1st dan in online mode you must be doing ranked matches. If you get to 1st dan from battle points, meaning you lost a couple of times along the way or you lost on your promotion match you will still have the title of 1st dan but not the achievement itself. For the achievement to unlock if you are 1st dan or beyond requires you to simply win a match.
Another thing to note is that in your ranked match options you typically only want to face people three ranks above or below you. When you click on Ranked Match change your rank limits to either a yellow or green 3 to be safe.
Personally, I had 9 W / 11 L when I got to 1st dan in online mode.