I finally beat Arkham Asylum in one life on hard difficulty. It took 5 or 6 tries. I lost track after starting it over a year ago and then giving up after about 4 attempts. I picked it up again not long ago and, after two attempts, I did it!
Here is the run. I took my sweet time, so it is over 5 hours long. However, I found out that it can be completed in less than 2 hours via speed-running (glitchless), which I will begin to work on soon. Until then . . .