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From ps3trophies.org:
I recommend setting up a speed lap
session with 99 laps in, this will
then give you 99 laps to try and beat
the required lap time.
TURN PILOT ASSIST OFF!
The best route for this trophy would
be:
Do 1 lap around and save your speed boost. As you get near to the
starting/finishing line you should use
it. This gives you a big boost and an
extra valuable second on the next lap.
As you go around the first corner try to hit all 3 speed pads,
the first is in the middle of the
track and the following two are on the
outside lane. After you have hit the
last one try to move your ship back to
the left hand side of the track.
Now there is a bum in the track. If you hit it right, tilt your ship
upwards & use your speed boost, you
should be able to fly into the air
giving you enough time to do your 1st
barrel roll.
As you land a barrel roll you get a speed boost. Hopefully you will
land at the top of a ramp going down
to another part of the track. You
should fly off of this giving you some
more air that will enable you to your
2nd barrel roll.
As you land try to hit the speed bump and fly close to the right hand
side of the track to turn the corner
nice and tight.
THIS IS NOW THE HARDEST PART TO PERFORM!! As you go around the left
try to hit two speed bumps in one go,
head to the left after the speed bumps
to the high ledge shortcut. Head to
the RIGHT of this ledge where it is
slightly higher, you are aiming to try
and get high enough to quickly perform
your 3rd barrel roll. You need to
quickly do the barrel roll because you
only have about 1 second air time, as
you come back down try to maneuver
yourself back into the middle of the
ledge.
Now try to keep on the ledge for a few seconds until you have to jump
off of the left hand side, here you
will have to perform your 4th barrel
roll. Try to land on the speed pads at
the bottom for a further speed boost.
Now just cross the finishing line and
hope that your time was under the
required target.
This is another trophy that requires
you to have patience but with practice
you should get it over time.
Finally, this is the suggested video to follow for pinning down the precise barrel roll locations: