In lack of better knowledge, i will recommend doing this in Co-Op vs. AI
. And just shotgun all the way. It's probably not inconceivable to get 30-50 kills per match based on your skill. Grind all the way to the 5000 kills.
I've made a tool accessible online. It shows your exact progress towards the 5000 kills.
Write me a message if it doesn't work for you.
Find it at https://xbltracker.com/