This achievement requires you to finish the game with the difficulty set to "hard" without ever reaching the continue screen. This may seem very difficult at first, but there is no restriction on what other settings you change. So to put it simply:
1) Set difficulty to Hard
2) Set player stock to 5
3) Set bomb stock to 5
4) Set extend type to every 25,000,000pts
5) Have fun with the game!
With these steps, anybody can get this achievement with just a little practice. You don't have to be some crazy 2D shoot'em'up god. =P