This is best done with a friend otherwise it could end up taking you some time. Regardless, the first step to obtaining this trophy is to complete an online game, personally I saved a film from ranked after doing my fight requests however the choice is up to you. In order to save a file, you must click up to the battle log. It's on the upper left portion of the screen. Simply save one of the battles listed here and then go to "My channel".
Set the lobby to a broadcast style and leave it open on the off chance you could get a download from a random or two. If you're doing this with a friend, click "Friend Invite" and click x until your list pops up, click the recipient and then click right and x. Repeat this 20 times until you see "Total downloads" reach 20.
DO NOT LEAVE THE LOBBY BEFORE REACHING 20. IF YOU DO SO THE PROGRESS WILL NOT COUNT.