i always use a cheat in the beginning of the game. as soon as you do this cheat you will be able to 1CC this game as you dont have to upgrade your weapons or speed. when you start the game and your ship is flickering you can do this cheat.: Up, Up, Down, Down, Left, Right, A. now your speed is fast, weapon is full but you can change it for another one, and your bomb is the best one, the one that goes straight and makes a big explosion.
one tip i got for you is that a lot of times when you see an upgrade its actually for that peace of that level so it makes it easier for that part of the level. but you dont neccesarrally need to do that. you can use the strongest weapons for that too. personally i find them great for finishing the game quickly, sometimes even 1cc the game. quickly still means about 40/45 minutes or more even.
best bomb is the one that goes straight and explodes to make a big explosion that will stay in that place for a few secs destroying anything it comes in contact with. best normall weapon is the laser that goes straight forward with the circles around it. this strongest weapon along with the strongest bomb enables you to quickly finish your opponnents of, if you decide to use the super bomb (A+B) it will ussually take the life of even the bosses in 1 shot. even if you do this you can still cheat in the beginning of the next level so your full power again.
i ussually dont cheat in most games but pulstar sucks hard without this cheat. it takes around 2 levels to fully upgrade your ship and all of that is gone ones you die ones. so i always start with this cheat thus making it a little less stresfull for myselfe.