There are several ways to resurrect a Sim. By far the easiest way is to use the karma power 'Divine Intervention'.1. GET POWER
First of all, pick up the following [easy] achievements (first is a MUST, rest give you challenge points towards buying the power):
Then, press the back button and go into challenges (far right). Now press the X button to go to the challenge shop. At the top it will tell you your available points.
If you have less then 125, you'll need to go and take a tour of the military base, the science labs, the city hall and the movie theatre (press back whilst playing and go to the town map, press A on each of the above and select "tour of ....").
If you still have less than 150 challenge points, now go to the graveyard at night and talk to a ghost.
If you followed the above steps, you're all set!
Go back to the challenge shop and scroll down until you find "Karma Power: Divine Intervention". It's worth 150 and comes shortly after a bunch of outfits. Buy it.2. KILL SIM, USE POWER
Now if you're using a household with only 1 Sim, you'll have to convince someone to move in with you. Or you could just go and start a new game with at least 2 Sims in it (make one an Elder).
The achievement will unlock when you use that new karma power on a dead family member sim. There are a few ways to kill Sims. The easiest way is simply to make one of your Sims an elder when you create the household and turn the aging up to the maximum (press start, go into options and slide the 'Sim Lifespan' bar to the right). Keep playing for a few days and your Elder sim should eventually die of old age, and will be replaced with a ghost.
If you can control the ghost like a normal Sim, you did it right.
Press back button and go into karma powers. Select 'Divine Intervention' and cast in on the ghost.
Note that Divine Intervention costs 75 karma to use. You should get this much just by playing the few days it takes for the sim to die. If not, the ghost will hang around for five
in-game days, so try to complete a few wishes for extra karma.