There is no upgradeable score system in this game. It's all about shooting enemies and picking up coins they leave behind.

Enemies killed with the standard weapon, will leave silver coins behind.
If you shoot enemies with the "dragon shoot", they release gold instead of silver coins. Gold coins are worth the double value.

It is important to distinguish between shooting enemies by the seperated dragon or penetrating them by releasing the dragon. This is called the "dragon shoot". The dragon needs to "rush" through the enemy to turn your reward to gold.

A nice challenge that gives you additional 30'000 points if you successfully kill the boss in the right moment with a "dragon shoot". Here's how:

Wait for the boss' second form of appearance. At one point his chest opens and you can see his beating heart for a short time. Needless to say that in this moment the boss enforces his defence and turns the screen into a real bullet hell. Find your path through the bullets and shoot the dragon from a close distance through the boss' heart. If done correctly, "Technical Bonus" will be displayed in big letters and you are 30'000 points richer.