Here's my guide for gold stars, which is 800k and 100%. This is the version with commentary, explaining what I'm doing and generally why I'm doing it. I've also uploaded versions without commentary, which should be linked on the video page.
On hard, enemies shoot more often and deal double damage. On Passion, there's also some rearranging of enemy types; most notably, in the beginning, instead of gears, you'll get fliers to octalock. Passion's easily the biggest shift from Normal to Hard, and getting pummeled is going to be a problem. Health is going to be a concern, especially at the end.
The most important thing to remember is to keep your perfect multiplier going! The multiplier only counts for octa-locks, meaning you'll get minimal points for spamming. For gold stars, you'll want a combination of octalocks and spamming, but if you're not going for gold stars, it's best to always try octalocks, even if the enemy is about to get away. Your purification percentage takes the hit, but you get a few more points out of it.
Passion's probably the hardest to deal with. Get a x8 multiplier off the cores in the very beginning, it'll help boost early. The satellite will probably take the most practice to master; if you take too long, it starts shooting at you and you lose the 100%. If you're going for gold stars, take time to line up octalocks, but if you take long, you may want to spam. Getting that sense of timing just takes practice, unfortunately.
For the boss battle, chances are you won't be up to snuff on points. Only octalock the orange core and don't fire on the purple to prolong the battle. Because of this, you'll need to be very good shooting the patterns down. On Hard, a few still managed to get through to me, so the rest of the stage needs to be an A game because of this.
Also, if you're having trouble with octalocks, turn down the sound effects in the main menu. I dropped it to about 20% and the beat was very clear for me.