This is pretty easy. I used the slow fighter with the first shot option, the middle missile option, and the first behind option.
Note that your score constantly increases as long as you fire, so always be hammering
for extra points.
Proceed through the first level. Pick up power ups and stay alive, as the only real danger is slow moving orange bullets. Stay to the back of the screen and avoid them. Your missiles will fire at 45° angle so use them strategically to destroy ground enemies while shooting ships in the air.
Once you get to the boss, simply stay at the left side of the screen while shooting at him and avoiding the orange bullets. Don't worry about maximizing damage on the boss- you actually want to minimize it, shooting him with your straight shot from a distance and milking a ton of points in the process. Things won't get too hectic until his final phase, at which point he fires more bullets. Once you get to 280,000, burn him out with bombs and you'll be put over the top when he dies.
Here's a run where I died twice at the boss but still easily made it to 300,000:https://www.twitch.tv/videos/160598051