Before you can attempt this achievement, you must be a Rank 10. Now Lester will give you a call, so head over to his house for a short cutscene where he informs you about Bounties. Load up a Private Lobby with a friend who is also a Rank 10 and have each player call Lester. There will be an option to "Place a Bounty" on a player in the lobby for a minimum of $2,000. Place a bounty on each other and simply wait for 24 in-game hours (45 minutes real-time) to pass.
Be sure NOT to kill each other, or it will void the achievement; however, if an NPC kills you, it does not void the time. Furthermore, if you decide to perform any activity within the world, the timer will pause; so make sure both of you just stand still until time has elapsed.
Take note that you can get kicked for inactivity if you are standing idled for too long! To avoid getting kicked out of the lobby and ruining your progress towards the achievement, it is recommended to either cruise around the city in a car or hang out in your apartment - if you have one - until the achievement unlocks.
Alternatively, you can try to get this achievement solo if you do not have anyone to place a bounty on you. Often times, when you hijack enough vehicles during your online session, the NPC you hijacked will text you with a threatening message informing you that they are going to get back at you. Shortly after, Lester will call you and let you know that the NPC has placed a bounty on you. If this happens, follow the method above in order to pass 24 in-game hours.