Gilgamesh Requirements?

It seems that you have to make it to 12 minutes with around 320 kills to spawn him. Anything less than that and you'll have to kill all 431 monsters. I've tried this on multiple accounts and things seem to work according to that. That's the pattern I've found.

it may be random, because I had over 350 at 12 minutes and the mission still timed out basically with no gilgamesh