Sonic The Hedgehog 3

The 9th and 10th levels of the game are the Ice Cap Stages, these aren't that hard but take your time anyway. You have the advantage of a save feature that you can use to save your progress at any point in the game so if there's a section that you think you're going to die, save it and then attempt and if you fail, re-load the game save.

Simply complete these two acts to get this achievement.

This is the 5th Zone in the game, it is fairly easy to pass but the boss can be difficult. In the level you will come across purple trampolines simply jump up and down on them to move them to get to higher areas. When fighting the boss beware his ice mist, if he sprays you with it you will be frozen, so the odds of getting killed are very high. The best way to deal with Eggman is to attack once and then dodge the ice and repeat, it may take a while to get the pattern down.