To start an Interactive League game follow these steps:
Main Menu > Xbox Live > Online Game Modes > Interactive Leagues
Some people have reported this to be glitched, but this seems to have been fixed thanks to tattie:
"From playing tonight, someone quit on me so I went to their GC to send them an abusive message and it said they were playing an Xbox Live game, I know for sure when you play in the Interactive League it actually says I.Leagues, so I thought these games are counting as ranked and not I. Leagues.
More evidence, I have played I. League matches where if its a draw at the end of the match it ends because its a league, you don't do extra time, but some of the games do go into extra time which leads me to believe the MM system is not giving you I. Leagues all the time.
I believe this big bug only happens in the German leagues as I only have ever won 1 game in the French league, and got the achievement after winning in Germany.
To make sure you get an I. League match, Private Chat someone and ask them to view your GC while you play and if its says I. league, win the match. I can also confirm that you have to win a match in each league.
Basically, you know if you had a league match because when you press start it says "Return to League Community Screen."