Timed challenges are only available online in a freeburn game.
Firstly make sure you are driving the Boost Special car Hawker Mech
and either enter or create a game and once someone is in your game start a timed challenge.
Once the challenge timer is running hold your boost button (
) and press the
to cycle through the 3 boost types (Stunt, Aggression and Speed).
And providing you complete the challenge the trophy will be yours.