Yes the time constraint can be difficult. You managed to stick to and polish the core gameplay quite well.
Stamina, health, damage - I hope you find an immersive way to convey this information rather than slapping on a set of numbers in the corner of the screen.
When the tops collide, create some sparks or ripple like vfx; perhaps increase the vfx intensity depending on the level of damage inflicted.
Btw are the players meant to fight as many tops as possible? In nearly every round, I just moved around the ring waiting for the NPCs to destroy each other and then I took out the last one with ease.
Playing again, I felt that it might be nice to have the default view slightly zoomed out so that a bit more of the ring would be visible, but not all of it (leave some room for "exploration"). To be honest, I felt nauseous a few times when I was going around the ring a few times. It might be worth a try to have the camera static, although I think it might affect the "action" aspect of the gameplay due to reduced camera activity. You could also give the player the option to zoom in and out, set camera to static or whatever. I guess playtests might help. You do you.
Good luck!