Buzz!: Brain of...

There are 5 channels you'll need to play through a full game on to get the trophy. What the description doesn't state is that you must also play a round of each catagory within that channel.

The 5 channels and catagories within are:
MUSIC -
Rock Classics
Lucky Dip - Music
Golden Oldies
Dance Anthems

MOVIES AND TV -
Kid's Stuff
Lucky Dip - Movies & TV
TV & Drama
Australian Cinema

KNOWLEDGE -
Lucky Dip - Knowledge
People & Events
Around Australia
Popular Arts

SPORTS -
Sports Stars
Team Sports
Lucky Dip - Sport
Motor Sport

LIFESTYLE -
Fashion & Design
Toys & Games
Lucky Dip - Lifestyle
Food & Drink

You DO NOT need to play the MYBUZZ! Questions channel (and cannot now anyway due to server closure).

*Please note that this is the Australian version of the game so other regions may slightly vary with some catagories.

Also, as the servers have shut down on this game now I believe the only way to get this done is through the WITH FRIENDS option which is basically the local multiplayer option. I don't think you can select a specific channel when you choose the BY MYSELF option.