Before you can even attempt this trophy you need to first unlock the Nitrous upgrade for your car by completing the first race for the car in the Easydrive menu.
Once your car has Nitrous equipped used a Bodyshop to fill your nitrous bar or perform stunts to fill it.
Once filled find a long stretch of road and from a stand still hold
and
to perform a boost, keep holding till the boost bar is completely depleted and the trophy will be yours.
Here's a video