First off, you need to unlock the Ovoid ship.
To unlock the Ovoid ship, you will need to collect 2 pies in one playthrough. It can be done on any of the difficulties at any speed.
The fastest way to collect 2 pies is on Level 1 and 2.
On Level 1, when the game prompts you to go right (right side of screen) or straight (left of screen) stay on the right side of the screen to enter a sort of free flight. After you enter the free flight you will want to keep your ship on the left side of the screen to head dead East. Eventually once you fly East enough you will see a pie start bouncing around the screen with MBG on it. Shooting it will produce score points, but make sure you actually maneuver your ship over it to pick it. After picking it up continue to finish the level.
On Level 2, do the exact same thing. Right side of screen for free flight, head dead East. Again you will see a pie bounce around the screen, the difference with this pie is that it will produce 1ups if shot, but again, make sure you actually pick up the pie. Continue to finish the level.
Once you complete Level 2, you will have popped these two achievements:
and unlocked the Ovoid ship.
Now, simply start another campaign and choose the Ovoid ship at the ship select screen. Can be done on any difficulty and any speed, Score Tilt mode will not work for this. The achievement will pop after completing Level 4.