A barrel roll is rolling your car in midair then landing on your wheels. Simply rolling your car won't cut it so you'll need to find a ramp and a decent car, there are plenty of hills in the desert areas you can use, there are also multiple ramps at the graveyard in 'Take Me To Church' and in other places around the map. Once you have a ramp and a car, you'll need to hold and / in midair in order to roll, if you land on your wheels (or close enough, there's a little leeway) you'll get this trophy.