How can I make my new kitten have a bit more of a healthy killer instinct?

I recently got a new cat and two days ago, I baby seagull has has damaged its wing and is unable to fly and it's been hiding in the bushes in my back garden.

When I saw this I took the kitten outside in the hopes that her feline nature would come through and she'd attack, play with, kill and then eat the seagull. I was hoping to film the encounter and put it on my YouTube channel about spiritualism but unfortunately the seagulls mother swooped down and attacked my kitten and shook her up pretty badly.

After a few attempts I managed to hit the mother with a small stone and she's flown off and not come back again

However, my kitten is now too shaken and scared to attack the baby seagull even if I put her really close to it. I've been trying with her quite a few times but unfortunately my sweet baby girl is just too shy to go near it. It's really starting to bug me now because it's summer ATM and I want to sleep with the windows open but if I do, the baby seagull keeps me awake with it's pathetic pleas to it's mother. I'm hoping that as it's not eaten, the seagull will get weaker and that my incentivise my kitten to let nature takes its course but if it's sunny tomorrow I'll want to go sunbathing so I don't want this to go on much longer If it wasn't against my ethics and spiritual believes I'd just kill it with a shovel to put it out of its misery but I'm forbidden to kill animals (or dine on their flesh).

Is there anything I can do to make my cat fierce up?