Stage 1 was by far the hardest for me to gold star. I just did it on Hard, and while there are some changes, you can mostly use the same strategy.
Some things to know about stage 1:
1. Right at the start of the first section you can miss a wave of enemies if you don't kill the jiggly orange guys fast enough. I think it's the third wave specifically that you need to kill quickly, otherwise the 4th won't spawn.
2. On the section right after, only do 8x octolocks on the giant worm dudes that fly around. When the smaller enemies come flying in, just kill them by rapidly hitting A as fast as you can so they don't fly away.
3. On the section before the mid-boss, you can miss enemies if you don't give them time to spawn from the orange cubes. This was only a problem for me on the third phase though, so just give it a little time so they all come out.
The area after that with the walls is easy to do.
4. On the next area, the one that leads into the boss, it's easy to miss the small flying enemies as they spawn out of the spheres that you have to destroy. It's usually the third sphere where I would miss the enemies, but I found that if you kill the two that come out on the right side quickly, you can take out the other 3 that went to the left before they run away. And then 3 more (IIRC) will fly in, so just kill them as they come in. Then you need to kill the giant worm that's flying around, because if you don't do that fast enough, one of the purple worms won't spawn from the bottom sphere. There should be 2 of them. And then the rest is straight forward.
And when going for gold stars, just aim for 700k score because if you save the 3 bombs, you'll get 100k bonus at the end. If you find yourself ahead on points, you can use a bomb to clear out enemies before they escape, but having two bombs at the end only gives you 50k bonus, so it costs you a decent chunk of points.
