I'm playing ESPGaluda for months now and it's cool as hell. It's one of the best Cave games I've played except for DonPachi and ESPRade.
The normal gems you get by killing enemies with your standard shot/charge shot increase your slowdown mode time counter. In slowdown mode, all bullets of enemies you destroy turn into gold that floats back to you for some extra bonus between rounds. For good scores/multiplier boni, it's important to concentrate on enemies that release huge bullet swarms, for ex. the trains or bigger tanks.
Also, the super/charge bomb does way more damage in slowdown mode.
Once your slowdown mode counter runs out, the speed will be doubled (compared to normal mode) and the bullet color changes from pink to red. You can still use the charge bomb tho, so it's not unreasonable to stay in slowdown mode (or speedup mode in this case) while in a boss fight if you want to nail the boss as fast as possible... of course the bullet patterns become even more deadly, but that's not important if you're going for a super blast because you're invincible while charging.
However, with an empty slowdown counter, you will get no bonus gold in return, or only a little bit to be precise (about 10% of the normal amount).
As a rule of thumb, it's enough to collect about 100 to 150 normal gems in the first three levels to get enough slowdown mode time, but later levels demand a more economic gem handling.
Apart from gold bonus collecting, the slowdown mode helps you to dodge more tricky bullet patterns which becomes important in later levels.
I also had my share of fun with the final boss, but after thinking about it, it's only logical that they don't allow killing him while in slowdown mode because even the mesmerizing criss-cross bullet streams of the end boss wouldn't be too hard to dodge... I just wish I could use the charge bombs.
So far, I have no useful strat for the end boss, perhaps I should get me one of those superplay vids.