For this trophy you need to set the fastest lap time of the entire race on your first lap.
Obviously easier if you set the game's difficulty to 'Very Easy'.
Once you start a Time Attack event drive as fast as you can on your first lap to set a good time that's well ahead of the other racers, then on the other laps (However many there are since this can be done in career easily enough) take it easy so you don't beat your previous time.
Trophy will pop at the end of the race