Complete the GTA: IV storyline in under 30 hours. After completing the final mission, you will enter free play mode, where you can complete any side quests or hooker killing that you may have missed. One of the best ways to save time is use taxis to travel on your missions, as you get there instantly, and they don't contribute time to the game clock. Watching cut scenes also contribute to your game time, so if you are running out of time, yet want to know the story, you can watch the story, then reload your last save, start the mission again, and skip the cut scene to save valuable minutes.
You can check your progress:
Start--> Stats--> General--> Playing Time
**Note** This achievement does not unlock until after the credits. Once the game is over, the "You Won!" achievement will unlock, then you after the credits will come "Liberty City Minute".
For more advice and discussion, please see this thread: