This can be obtained in the online or local multiplayer mode (not local co-op)
You will need 2 controllers to obtain this in local multiplayer, if you only have one then you will need to obtain this in online mode against another player.
Simply play all 4 zones: Emerald Hill, Casino Night, Mystic Cave and Special stage.
The zone will end once both players complete the 2 acts in each zone, if there is a tie (both players won a level each) then there will be a third round which is a special stage to settle the tie.
If you're doing this solo with 2 controllers then you'll need to navigate either character to the end of the level and wait 60 seconds for the other player to run out of time. There shouldn't be any need to touch the 2nd controller.
Luckily the game crosses out each zone as you do them so it's easy to keep track.