I came back to play this to finish my medal collection for this game.
Turns out this game is a lot easier than I thought when I first played it, but it requires a few fundamental, if non-intuitive changes in the way you approach the game because the various graphical effects don't give intuitive feedback:
1) The laser slicer can only hit one target at a time. This includes body parts of dead zombies! You can shoot zombies from offscreen, though not recommended as it seems to create dead bodies that stand upright and thus block subsequent shots.
2) Unlike most zombie games, you need to aim at the body, not the head. You must also be careful not to aim at the hands. You can see if new zombies have spawned by checking the number on the bottom left.
3) The zombies spawn when you step on invisible trigger points, and will drop down from fixed zones in the ceiling. Therefore, do NOT rush ahead blindly, kill the zombies as they come until they stop spawning entirely before proceeding. This prevents you from getting swarmed and helps with not knowing the number of zombies you need to kill per stage.
4) While you do need to charge the laser, it doesn't need to be for as long as the sound effect suggests.
5) If you have a bit of trouble evading, try jumping. Its not perfect but it will help reduce the damage and if the zombies punch you, it will help push you away from further damage or from getting ganged.
With these, I was able to beat all levels without dying and thus get all medals. Hope that helps future players!
I have played the later Pico version of this game after this review. The same points largely apply, though headshots are no longer penalized and that makes the game significantly easier.