Before you start your first race you'll have the opportunity to do a hot-lap qualification by pressing the
button.
Screenshot is from the Xbox since I only have the Xbox version but I imagine the solution is the same here, just the
button instead of the
button.
Make sure to qualify to start from pole position, shouldn't be to hard on the standard settings.
If you can keep ahead of the pack, thus not taking any damage, you'll pop the trophy when you finish.