Be careful with this one as it has the potential to screw up your game.
You can kill off a Sim in a number of ways: starvation, drowning, by fire, etc. The easiest I've noticed is to create a small room with a sim and once they're in it, delete the door. Place a fireplace in the room as well as a rug and start a fire. Keep poking it and eventually a fire will start, setting the rug on fire as well. Since the room is small, this will catch the Sim on fire and with no door, they'll eventually die. Keep their gravestone there and eventually their ghost will return.
Now's the tricky part. You'll have to unlock the Karma Power for resurrecting a Sim, which costs 75 Karma. Once you do, use it on the Sim to resurrect them and you'll get the trophy.