This achievement requires that you complete the game from start to finish in 3 hours. Note that this is 3 hours on the game progress statistic (Shown when you save), not in real-time, so you can pause, save, load, leave, come back, etc without negatively affecting the time.
Remember that you can skip most long cutscenes and dialogue by holding Y. Skipping most cut scenes and making a couple of mistakes will net you a time around the 2-hour mark, so you should have lots of time to spare.
If you want to use a walkthrough just to seal the deal, I recommend this one:Monkey Island 2 Walkthrough on GameFAQs
Dot-point, very short and to the point, making it easier to read while playing, full credit to Headrock on GameFAQs.
EDIT: The above guide is missing the following step: At around step 16 in chapter 4, open the barrel beneath the parrot for the third cracker.
Best of luck!