yes, you heard it correctly: you must do at least one of these requirements, no need to try to do them all
(heard from LtC that the 50 million points or the 270/300/330 hit chain is the less hardest, just a note, boss chains don't count for this criteria; I've seen that for myself once when I 1cced the first loop)
trying to explain a bit about scoring (at least some basic stuff):
- ESP Ra.De: when you use the secondary shot on enemies, there are attack splashes; finish that enemy with your primary shot, and the enemy will release point items; the more splashes on the screen when the enemy is killed (by your primary shot), the greater is the multiplier (up to 16x); the more resilient the enemies are, the longer these splashes last, meaning that it's easier to get multiplied points from them (said multiplier lasts for a while, as well; for example, there are certain yellow ships at the School stage, that consists of three parts; don't shoot them yet, perform a multiplier on a different enemy, then attack these yellow ships with your primary shot and they'll release multiplied point items)
- Armed Police Batrider: killing enemies with your Aura (the aura that forms in front of your ship when you don't fire for a couple seconds, not the shot while the Aura is active) or the Bomb often yields more points than if you killed them with your shot. The game has a medalling system, in which the next medal that's generated on the screen will be worth more than the former (100/200/300/400/500/1000/2000/3000/4000/5000/6000/7000/8000/9000/10000, I think..), but if you let one medal fall from the screen, the medal level is reset back to the 100-point one (however, letting one fall from the screen while there are other/others still give a chance for you to maintain your current medal value, if you grab the medals that are left on the screen. Due to this, it's important to plan out when to get ground-based medals, because they scroll way slower and can be used to fix such mistakes); certain stage triggers (example: destroying the house in the first stage and then the billboard, instead of the billboard first, destroying all of the triangle-shaped ships in the Sky High stage and having a Mahou Daisakusen character alive by the end of the same stage) or character selection will allow you to fight additional bosses, that can be milked for score
- Dodonpachi: performing chains, bullet-cancelling (stage 3 and 5 have enemies that clear the bullets on the screen when they're destroyed), having the Maximum Bomb bonus (it seems to add your current "max hit" x the current multiplier -- 1x, 2x, 3x.. I think that using a bomb and then collecting another and thus entering the Maximum Bomb bonus will give you 1x bonus, which is why people avoid using the first bomb on the first boss -- to your score, per each 1/60th of second); the minor scoring factors are the bees (they increase in value as they're collected without dying, but their value is reset across stages, unless you've collected all of them in the same stage, in this case, their value will be one level higher in the next stage), and the stars (they're lost if you lose a life, and their amount is reset across stages, unless you're using the P2 ship). The P1 ship has the advantage of being able to increase its Boss Chain counter by using the focused bomb, but the P2 ship is said to be "for the people who don't die", due to the already mentioned benefit of the stars' amount not being reset across stages