Work on your upgrades
In the first few levels, try not to get hit or use any of your special moves. This way you can focus on upgrading your attacks and healing powers for when you need them. It might be easier to shoot your way out of a level, but playing smart will set you up for later in your run. Make your shots longer, make your dash go farther, and when there are more enemies on the screen you're going to be in a much better position to take them down without dying.