I'm making up for the last 10 games which I sucked at.
It's definitely one of those games where you can get a bit further each time just by knowing what's there. The first time I played I didn't even get up to the first grey boulder thrower, so I gave up. Then my brother had a go, and he was a bit more persistant. Eventually we figured out how to recall the ladder, how special items worked, and that the ladder length depends on how high the screen is. We always took on the first boss (the water spirit) with big fireballs, but we soon learnt that you could just spam triple fire and it would be dead before it could land its first jump. Nearly all the enemies in the game can be killed quickly just by shooting fast (centipede woman and t-rex are probably the two exceptions). Mummies can't be killed, but you can play through without ever facing them.
The bat trap in the middle of stage 2 had me stuck for a while, followed by the blue birds, then the volcanos at the start of stage 4. There was a younger kid at the arcade who was good at it, and we learnt off each other. He was the first I saw who made it to stage 5. Stage 6 is pretty hard going, and the middle of stage 7 had me stuck for quite a while. Stage 8 is piss easy, and stage 9 is mostly about getting to the final boss before the clock runs down.
There are a few cool things you can try with experimenting, like where the falling bonuses are. There seems to be a lot more in the US romset, particulary speed boots. If you activate speed boots while you're jumping, you do a kind of super jump. Another interesting trick is climbing the towers at the start of stage 2. As long as you kill the heads, you can safely use the body segments as stepping stones to reach the top path without losing your ladder. The rest of my techniques are in the INP file, although I took a few risks like not using the boomerang on t-rex.