It's a pretty straightforward game in which you can only employ one single tactic if you want to win – move to the opposite side of the screen out of the range of the fire breath and keep shooting until the “mushroom” jumps into your wall of bullets. Given your limited moveset, no room for mistakes and the unchanging attack pattern of the enemy, anything else will get you killed.
To improve the game, it'd be nice if the enemy sometimes did something different (especially as its health decreases) – but if it made the game significantly more difficult, you'd probably have to give the player lives, so it's not just a one-hit kill. And possibly allow jumping to allow for some added complexity in the attack patterns.
But as a simple game you play, win, and forget (or as an early-game boss in a larger project), this concept works fine.