To complete this achievement, you must beat an entire level, in either Story or Free Play mode, without dying. You can lose as many hearts as you wish, you just can't die. The easiest level to do this on is probably "Escape the Mines," as there are just a couple of enemies in the beginning, and it is clear from there.
Another possibility is the "Well of Souls" level, the only tricky part is the boss battle against the snake, but if you know what you're doing, you'll be safe. Stay on the platform in front of the snake, and toss torches at it until it is dead. A third possibility would be "The Hunt for Sir Richard." These three levels are probably the easiest, but it is all personal preference as to which level you are best at.