The objective of unlocking this achievement is to beat the game with five lives, a clever phrase for beating the game without continuing or successfully doing a 1CC (1 credit clear) run. The key thing to remember when trying to get this achievement is to turn on the move guide feature so you can anticipate the moves coming up.
Because the achievement is a 1CC achievement, you can afford to lose up to four lives going through the entire game. Once that fifth and final life is lost, the opportunity to unlock it has past and you will have to start all over to try again.