I beat the first score challenge! If you're interested here's how I did it:
1 - you must hold the R button at all times so that you don't miss any of the blue tokens that appear when you kill a wave.
2 - you can't use the secondary weapon (B button) because that way you won't be able to add up multiplier to the bonus points you get when you kill a wave.
As for the concrete level strategy, I started with the first weapon until the first large ship appears. In this section I killed every single enemy.
For the second part I used the third weapon, killing almost all enemies leaving behind just a few of those things that have a pulsating green light around them.
When the last large ship appeared I switched again to the first weapon and stuck with it until the boss.
To kill the boss I used the last weapon. In the beginning I stayed at right-end of the screen because the last weapon has auto-target but for some odd reason it only locks-on for the boss's right weapon. Then proceeded to destroy the second pink laser firing cannon and since there were no more blue tokens to collect I used the secondary weapon and bombs at will until the ****** was dead.
It was tough but it was immensely gratifying, this game is hard as hell!