In addition to the free HP beside the round 2 star location, there are FOUR further free drops that are easy to get for beginners. This should make completing your first runs much smoother because you can avoid game overs and even consider some i-frame mashing damage on some bosses.

For round 1: drop your jetpack by the bird, crawl into the space, and shoot the back wall until HP appears.

For round 3: once you get to the underworld, kill the chyme (circled), grab its pointball, and fly over the platform for the HP to appear beneath it, drop jetpack, and crawl in.

For round 4, shoot the right side of the warp platform in the overworld after the Akubutsus.

For round 5, shoot the right bricks beneath the underworld portal.

NB: On more than one occasion I've seen the HP in 3 spawn in without the preqrequisite actions. I believe this is due to something I shot/grabbed in overworld, because I've also used the same idea to despawn bullets from the top cannon before the exit in 4 by doing a small delay after crossing the skull, keeping something on screen long enough that the game can't draw bullets for top cannon.

If you want to get enough score to get max rank and upgrades, avoid all stars - you'll loop back to the first stage and can grab HP ad infinitum. If you finish loop one with n stars, you will start loop two at round n+1.

NB: Don't die by falling in holes if you do this, or you lose all that precious HP.