Firstly when you die you may get your previously empty bomb and strikes back.

From what I've seen the blue beam is the best power-up, and can be stacked up to three times.

On the bosses once you can hit one spam the bomb button (Y/Triangle) which will cause any projectiles to despawn. Then use all of your strikes until you run out.

If you're terrible (like me) and die during a boss you may get more bombs like previously mentioned so use those. You can even die on purpose during a boss to get this done faster, but can be risky. Lastly after the first boss you typically have to outrun the crashing boss while dodging enemies. Just hold up until you die. It will not only end the stage early, but also won't make you loose a life due to this section being a bonus.

Only other thing I can think of is keep spamming fire when loads of enemies are up, and if you're in a less tense part with fewer enemies then shoot at a lower rate until more appear that you can't handle without spamming fire.