Hmm.

By accepting that reality just is. After all, why would it be any
different for us than for anything that is alive? Bacteria die daily,
never heard anyone suggest that they somehow live on. Life is discreet
- it has a start and an end. Many people feel that it would be somehow
lessened if it didn't end (I'm not one of them, by the way).

I do understand where you are coming from, however, the trick is to
realize that there is nothing to fear, after all, you were always going
to die and you accepted the notion with (presumably) no problems until
now. Were you religious? If so, in what way did you think differently
about the fact that you would die? After all, even in religions such as
Xtianity, were it is taught that whilst all believers die, they will
eventually 'live again' after a certain event has taken place, people
still die and the 'after life' is not described as being the same as
actually being alive. In fact it tends to be a rather nebulous notion
at best, but that is an aside - you still were going to die first.

I don't actually understand why you find it so nightmarish, I suppose is
what I am really saying. On a slightly different note, I make the most
of my life, in part, precisely because it is the only one I have.