In online freeburn, start a challenge if you are the host by going into the online shortcuts menu with
and selecting the Challenges option. You can choose from Timed, Freeburn or Island challenges. Then select any challenge from the list. (The challenges you can pick vary with the number of players in the session.)
Once a challenge is started, you and the other players must follow the instructions at the bottom of the screen to complete it. Once it is completed you will have your achievement.
If someone else is the host and they start a challenge, you can complete it and get the achievement anyway.