To start off, you need to start the T. REX Chase mode. To do this, hit the left ramp (the one with the closed gate under the Jurrasic Park sign). This will open the gate. Once the gate is open, hit the ball up this ramp again to hit the car spinner. This will advance the car at the top of the table forward and will also close the gate. Repeat this process (open the gate and hit the ramp) 4 times. Once you reach the end with the car, hit the ramp again into a now opened hole labeled 'Tour'. You now have to choose Malcolm's Path to start this mode. Once started, hit the same ramp repeatedly in order to move the car further away from the T. Rex. You have about 15 seconds between each shot, but you need to be much faster than that to complete the mode in time for the trophy. Once you hit the ramp enough times and in under 40 seconds, you will complete the mode and unlock the trophy.
The first part can be done over multiple balls, but once you start T. REX Chase, you need to complete it in one ball.