Brawl of the Week is one of the options available after selecting online play (for me it was also Kuung Ball so could be accessed from the top menu) and can also be reached by pressing Y to open settings at the top and selecting it as an option
You don't need to be the same character in the games, nor play against the same person, or win - just play three full matches. The bot match beforehand doesn't count.
If it's your first time, do remember to check your corner menu and see what the daily mission is as this can help towards your gold collection and also legend progression