Good concept, this was very challenging!
It took me a second to realize that defeating enemies extends your timer, even though I have the same mechanic in my submission lol.
I might be revealing how much suck after a few tries, but is it impossible or is there a trick to this?
The grapple and attack mechanics felt pretty fluid, I would suggest reducing the hitbox on the character a bit to make dodging bullets more forgiving.
Nice work!