I do not have a guide to how to earn this trophy legit however if you don't care about high scores and just want to get the trophy I have a solution. As soon as the timer starts counting down hold L1 and mash square, triangle and circle. After a few seconds one of the scientis will say the challenge is over successfully. You will be taken back to the challenge room area where you can get new guns. Just select the challenges you haven't done and do the same thing over again.
Credit to SMITH_UK85 on playstationtrophies.org.
http://www.playstationtrophies.org/forum/metro-last-light-re...