As mentioned in the road map, this trophy may be a little glitchy. If you feel that you have met the requirements and did not get the trophy, exit out of the DLC and restart it. Then do another run that beats the train. You may need to do this more than once. Thanks to BEN186422 for that tip.
The easiest route I have found is to board the train and ride it toward the finish. These are the steps:
1. Start running forward and double-jump, and Blink in between the 2 vertical pipes and the building slightly to the right hand side.
2. Run from here toward the shack with the glowing purplish light, and double-jump/Blink over and past it.
3. Run down the incline, and double-jump over the gap and up the ramp.
4. You should now be at the stone staircase, near where you found Emily’s doll on this level. Run up the stairs and climb to the top of the gate.
5. At this location, look left and see the train tracks above. It is possible to beat the train to this spot, but it may also be passing by as you get here. If it has already passed by, restart the challenge.
6. Blink up to the train as it is passing by. When you do so, it is possible to end up either on top of a car or between 2 cars. If you wind up in the latter situation, jump up to the car behind you.
7. Once on top of a car, make sure to crouch down by pressing because there is a low hanging obstacle near the station.
8. Once past the obstacle, use Blink to get to the lead car of the train if you have not already, and double-jump/Blink to the platform ahead of you.
9. Jump or Blink down from the platform to the white light that ends the challenge.
One general controls note, after Blinking you will need to press again to continue running.
This video shows the route and the amount of time you should figure on for this trophy: