You can "defeat" the Grim Reaper by saving a civilian after the timer hits 0:00. While this will likely happen naturally, if you want to speed up earning this trophy have one civilian with you and then wait just OUTSIDE the entrance room. Once you cross into the entry, the civilian will automatically be counted, so wait outside until the timer hits 0:00 and turns color to purple.
Then just walk in and once you get credit for the rescue, the timer goes back to 1:00 and the trophy will pop.