Death doesn't really draw near on his own accord: at least, I haven't been on a floor long enough for Death to start rolling in from lapsed time. For me, his arrival only happens when its been hastened by the 'no enemies present' situation, which has happened to me quite a few times.

Anyway, I'm defeated the second boss on this first level. Both bosses weren't that bad, it was basically a 'attack the weak point for an all-out attack!' type deal. I'm level 9, currently. How many floors are there to Tartarus anyway?