This is my first time entering an online challenge, and I want to make sure I don't miss the Enigma berry. So how and when do you access it? I've entered the comp itself and battled half a dozen or so times already.
If you happen to get a rank in the competition, you are ensured to get an Enigma Berry.
If you are one of the top 128 people who took part in the competition you get Championship points, but it isn't necessary to be one of them to get an Enigma Berry.
To get the berry, you must have atleast one complete battle in the tournament.
It's most possible that the Enigma berry distribution would take place after the tournament is over.
Hope I helped!