I've gotten some pretty amazing wins in Apex with at least 13 kills or more. BUT, somehow a level 47 can take my place as champion even if I did get a lot of kills. How does that even work?
This thread here talks about it being people who won their last game, and if there are multiple, the champion is the one that had the most kills. https://www.reddit.com/r/apexlegends/comments/at873o/who_are_apex_champions/
But if I remember right there was a discussion early on that it was mostly a weighted random because early in the game's life you would get 'champions' that were a party of 3 level 1 players.
Most of what I found were guesses. But I would guess that the reddit thread must be onto something.