I like the idea. It would need to be balanced so that other players actually have a chance at killing the stronger Guardian. There should also be a cap as to how strong you can get. Maybe every kill grants you a 10% increase in health. The health would be capped at 250% which would equal a 15 kill streak. A player has about 190HP in Crucible (I think, correct me if I'm wrong). So at a 15 kill streak the player would have 475HP. Usually it takes three body shots from a Hawkmoon or two headshots to kill the player; a bodyshot dealing 64 damage, a headshot dealing 94 (excluding Luck in the Chamber bullets). To kill another player at 250% health would take 8 bodyshots from a Hawkmoon, or 5 headshots. Not sure if this would be balanced, but I'm just working out the numbers, though I think this would be fair. I hope your idea is considered.