I didn't quite get what was happening until I saw the health bar. Game Over'd first time, picked a very strong damage upgrade and then beat it immediately. More audiovisual feedback would have helped and waiting for the weapon cooldown was kinda boring, so I'd recommend to shorten the weapon cooldown but make the clock a little tougher. This way the player has more to do instead of just waiting for the attack cooldown and it might feel more like it was the player attacking too slow themselves instead of the cooldown that makes one lose. I get that there is an upgrade for attack speed but it definitely didn't feel as strong as the damage upgrade that was like +37 damage or so. Maybe the balancing was off.
Either way, the game has a very lovely art style and the story is funny. Good job!