I think the cat should have said something about the upgrades.
I beat the boss with no upgrades since I didn't realize you could dash over the green slime.
Then the upgrades made the endurance match into a joke.
You beat it without collecting the items? I thought I made it impossible. Also, the cat is not to be trusted.
Hey, my bullets did damage, so I knew I could win. It took like 5-10 minutes, but I got it!
The key is to just camp at one part of the arena and randomly fire shots out. If they don't hit, oh well, you'll get it eventually.