Trevor is the only character you can do this with. After playing the story mission, "Friends Reunited," you arrive in Los Santos and will already be playing as nutjob Trevor. Round the block from Floyd's safehouse, you will find a drunk couple (displayed as a blue blip) who needs a ride home. This is the easiest time to get the achievement in my opinion.
Deliver them to the Altruist camp, which will appear as an A on the map near Chiliad Mountain State Wilderness (Northern Blaine County). Set a waypoint to the A, and follow the purple route, NOT the yellow one, the yellow one leads to the couple's house which will NOT get you the achievement.
The achievement will unlock once you deliver them to their DOOOOOM! A walkthrough video kindly provided by NEO182 is below, from his randomchievos channel on YouTube.
NOTE: There's a strange phenomenon happening just lately with the Achievement system on the Xbox One. Achievements aren't popping visibly or audibly, but they do. Your console has to be connected to Live, so if they don't pop, check your Internet connection, and the Xbox Live status page at http://support.xbox.com/en-US/xbox-live-status
They DO pop correctly, as I obtained them on the 360 version.