This pops at the end of the game when it shows your final score.
I highly recommend going for this on Arcade Extreme mode.
Whilst this is incredibly difficult, the game actually helps you.
For a starty, you can power up your weapon in the between-level shop.
Next, each continue you use sacrifices 50,000 points, but this doesn't matter, because you have a maximum of 99 continues to use. Despite you needing 1,000,000 points, the points sacrificed REALLY don't matter, because you get 1 million points outright for beating the 2nd form of the final boss, so as long as you complete this mode in under 99 continues, you're guaranteed the achievement.
I hope this helps!