How is the kill streak stat calculated for purposes of the two achievements (20 and 35)? Is it for killing every successive hostile you see, or every one you engage with, or every one that becomes aware of you?
It's just a chain of killing hostiles rapidly enough. Nothing to do with spotting, being spotted, or limited to those that engage you etc. Get one kill, timer starts, get another kill within X turns, timer is reset, continue until no additional kills before timer runs out and the final value is set.