Sorry it took a while but for what its worth...
I currently have 209 blocks so believe the badge would have been triggered on my 200th block.
I don't have a high block average as (unfortunately cause its not my favourite mode) my friend likes to play 2's and we often get on winning streaks and therefore have the ball most of the time... which means less defense = less blocks.
I suspect as others have said however that it isn't just block numbers... I imagine steals/poke ball loose, fouls/hard fouls etc probably play a part.
i also had a look at accolades (ie 2 and 4 blocks per game, 2 blocks and 2 steals etc...) and nothing else stood out as being a likely trigger.